1. science
2. social science
3. philosophy

To appear in Finding One’s Way Though Wittgenstein’s Philosophical Investigations,
E. Bermon & J.-P. Narboux (eds.)
SIMPLICITY AND RIGIDITY
READING SECTION 50 OF WITTGENSTEIN’S PHILOSOPHICAL INVESTIGATIONS
AFTER KRIPKE
Jean-Philippe Narboux
Draft
What I always do seems to be – to emphasize a distinction
between the determination of a sense and the employment of a sense.
Wittgenstein, Remarks on the Foundations of Mathematics, III §137
The standard meter in Paris would not be accepted as the
definition of the unit of length, if it were not protected from influences of
temperature, etc., by being kept in a vault. If an earthquake should ever
throw it out of this vault and deform its diameter, everybody would agree
that the standard meter would no longer be a meter.
Reichenbach, The Philosophy of Space and Time, §5
§1. In the first lecture of Naming and Necessity, Kripke singles out for criticism the
following pair of sentences from section §50 of Wittgenstein's Philosophical
Investigations:
C1
There is one thing of which it can be stated neither that it is 1 m long nor
that it is not 1 m long, and that is the standard meter in Paris (das Urmeter
in Paris).
C2
But this is, of course, not to ascribe any extraordinary property
(merkwürdige Eigenschaft) to it, but only to mark its special role in the
game of measuring with the meter-rule (seine eigenartige Rolle in Spiel des
Messens mit dem Metermaß).
Kripke regards this a “very puzzling” pair of remarks. The second of the two above
denials figuring in §50 is evidently meant to deflate, or at least to mitigate, the apparent
paradoxicality of the first. Kripke objects to both:
This seems to be a very “extraordinary property”, actually, for any stick to have. I
think he [Wittgenstein] must be wrong. If the stick is a stick, for example, 39.37
inches long (I assume we have some different standard for inches), why isn’t it one
meter long?1
1
Kripke NN p.54.
Kripke NN p.54.
3
Kripke NN pp.55-56.
4
Ishiguro (1969)
5
See Narboux (2014).
6
Two notable exceptions in this respect are Gert (2002), (2010) and Diamond (2001).
2
Kripke goes on:
Anyway, let’s suppose that he is wrong and that the stick is one meter long. Part of
the problem which is bothering Wittgenstein is, of course, that this stick serves as a
standard of length and so we can’t attribute length to it.
Be this as it may (well, it may not be), is the statement “stick S is one meter long”, a
necessary truth? Of course its length might vary in time. We could make the
definition more precise by stipulating that one meter is to be the length of S at a fixed
time t0. Is it then a necessary truth that stick S is one meter long at time t0. Someone
who thinks that everything one knows a priori is necessary might think: “This is the
definition of a meter. By definition, stick S is one meter long at t0. That's a necessary
truth.” But there seems to me to be no reason so to conclude.2
There follows an extended argument turning upon the central distinction of Naming and
Necessity, that between giving the meaning and fixing the reference of a designator, and
whose upshot is that the statement “S is one meter long at t0” (hereafter “L”) is best
construed as at once contingent and a priori.3 To the extent that to give a stipulative
definition of a designator (like “meter”) is to assign it a sense, the former notion inherits,
according to Kripke, the ambiguity concealed in the latter. Kripke argues that the
definition assigns “meter” a sense only in the sense that it stipulates what “meter” is to
refer to, not in the sense that it supplies a synonym for it (i.e. a linguistic expression with
the same sense). Given how “meter” is defined, S could not turn out not to be one meter
long at t0. But it cannot be concluded on this basis that S could not have failed to be one
meter. That we cannot make sense of the (epistemic) hypothetical possibility that S should
turn out not to be one meter long at t0 after all, does not imply that we cannot make sense
of the (non-epistemic) counterfactual possibility that S should have failed to be one meter
long at t0.
After having thus shown that, from the assumption that statement L has sense, together
with the definition of “meter”, it cannot be inferred that L is necessary, Kripke proceeds to
a second argument. He argues that it is in fact true that S could have failed to be one meter
long at t0, given that the length of an object cannot be regarded as an essential property of
it. From the truth of the statement that S could have failed to be one meter long at t0, he
draws the conclusion that L does make sense. Though still indirect in character, this
second, positive argument for the falsity of C1 is evidently stronger than the first, purely
negative argument against the argument to which Kripke traces C1. Finally, Kripke
adduces a direct argument. This third argument runs as follows: since stick S can be
measured to be 39.37 inches long by means of an inch-ruler, it would seem that, provided
that the conversion rule “1 meter = 39.37 inches” be accepted, it can be said of S that it is
1 meter long. (Note that this is by no means to claim that S can be measured to be 1 meter
long.)
The suspicion raised against Wittgenstein is that he may well have deemed L and ⌐L
nonsensical on the basis of a systematic failure to see how a statement like L could be
construed otherwise than as true in virtue of the meaning of “meter”. The possibility that a
statement of that form should be true a priori without, for all that, being necessarily true, is
obliterated from the start by his conceptual outlook. A lingering positivist bias as to how
to construe the conventionality of meaning will have kept Wittgenstein under the spell of a
dogma as to what definitions accomplish, The irony is that such a dogma fuels the very
sort of metaphysical illusion that Wittgenstein meant to dislodge.
This chapter divides into four main parts. In the first part, I try to demonstrate the
2
3
Kripke NN p.54.
Kripke NN pp.55-56.
2
philosophical (as distinct from the local exegetical) appropriateness of Kripke’s Response
to PI §50. In the second part, I bring out some of the difficulties that stand in the way of a
satisfactory reading of PI §50 with an eye to showing that on the whole they hardly have
been addressed by commentators. The third part is devoted to the Tractarian view of
simplicity. Drawing on Ishiguro’s seminal work on Tractarian names4, I contend that the
Tractarian view of simplicity stands much closer to the view of simplicity generally
regarded as that of PI §50 than to a Russellian one; and that it constitutes a first attempt at
construing simplicity in terms of rigidity. Finally, in the fourth part, I articulate an
alternative reading of PI §50, under which PI §50 bears critically on the Tractatus
precisely to the extent that it attains a more resolute understanding of the internal relation
between simplicity and rigidity.
I.
The Relevance of Kripke’s Response to PI §50
§2. Epigones of Wittgenstein have deemed it apposite to defend Wittgenstein against
Kripke by arguing that the point encapsulated in the above pair of remarks has simply
eluded Kripke and by mounting counter-attacks against Kripke’s own train of thought on
the matter. The latter’s epigones have generally granted the former’s claim to be speaking
on behalf of Wittgenstein. Thus, that the above pair of remarks can be safely and
unqualifiedly ascribed to Wittgenstein has generally been assumed, if only by default, by
both parties to this dispute.
Now, I think that these attempted rebuttals to Kripke’s critique on Wittgenstein’s behalf
can be shown either to be off-target or to misfire.5 They are to various degrees
uncomprehending. The dispute between epigones of Wittgenstein and epigones of Kripke
over the above pair of remarks is shaped by interpretations of both thinkers that betray
serious misunderstandings and are best treated as expedient foils.
But the basic exegetical assumption that is common ground to both parties – that
Wittgenstein’s thought here stands at odds with Kripke’s – does not withstand scrutiny
anyway. In this essay, I shall contend that this exegetical assumption can and must be
resisted if we are to attain a proper understanding of PI §50. Kripke’s response to PI §50 is
indeed predicated upon a misreading of this section. The main flaw of Kripke’s reading of
PI §50, however, does not lie in some failure to appraise the point of the above pair of
remarks, as epigones of Wittgenstein have been all too prone to maintain. It resides in his
outright and unqualified ascription of that pair of remarks to the author of PI, whereby he
fails properly to construe their function within PI §50 and to realize that his qualms are
quite congenial to the overall drift of PI §50 and the sections surrounding it. In other
words, Kripke’s reading of PI §50 is flawed on account, not of some failure to appraise the
point encapsulated in this pair of remarks per se, but of some failure to appraise
Wittgenstein’s point in having it made in the course of PI §50. In that sense, the standard
response to Kripke’s critique of PI §50 on the part of epigones of Wittgenstein has got
things almost exactly wrong.
Commentators of Wittgenstein have taken issue with Kripke’s ascription to Wittgenstein
of the paradox that is the subject of his study Wittgenstein on Rules and Private Language,
arguing (rightly, to my mind) that Kripke mistakes Wittgenstein’s dissolution of an
apparent paradox (which accordingly Wittgenstein by no means endorses) for the solution
of a genuine one. This makes it all the more surprising that on the whole it should not have
4
5
Ishiguro (1969)
See Narboux (2014).
3
occurred to those commentators that Kripke might be making the same sort of exegetical
mistake in Naming and Necessity in his discussion of “what Wittgenstein says” about the
standard meter in Paris.6 My own view is that Kripke is not wrong in thinking that the
second of the two remarks fails to mitigate the air of paradox assumed by the first; he is
wrong in adhering to the conventional view that Wittgenstein endorses these two remarks.
Concurrently with this uncritical assumption, the narrow focus of the dispute between
Wittgenstein’s and Kripke’s respective adepts on the pair of remarks that Kripke singled
out for criticism, coupled to a failure on both sides to read Kripke’s discussion of PI §50
against the backdrop of his overall philosophy, has induced a failure to discern the
relevance of that discussion to the issues of concern to Wittgenstein in PI §50.7 It has
obfuscated the perspective from which Kripke’s thought engages with these issues and
deflected attention away from the resources that Kripke’s thought affords for an
interpretation of PI §50.
For such resources to come into view at all, some convergences between Wittgenstein
and Kripke with respect to method must be given their due. In particular, Kripke’s claim
to be putting forward alternative pictures rather than alternative theories must be paid
more than lip service. This goes against the grain of the standard way of reading Kripke.
In what follows, however, I make no sustained attempt at fleshing out a non-standard
reading. Nor do I rehearse the grounds for holding that Kripke’s qualms over the above
pair of remarks, not only are to the point, but are in order. Instead, I set out to elaborate
and defend a reading of PI §50 that builds on insights afforded by Kripke’s thought. On
the proposed reading, the overall drift of PI §50 and the section surrounding it proves to be
quite congenial to Kripke's thought.
The reading of PI §50 to be developed here is meant to provide a genuine way out of a
certain exegetical predicament which I take to confront any interpretation of that section
and in which I take current interpretations to be caught. Accordingly, in order to motivate
my reading of PI §50, I delve into the sources of this exegetical predicament. In a nutshell,
the exegetical predicament takes the following shape: either PI §50 is shown to take issue
with the Tractatus’ picture of simplicity, but only at the cost of ascribing to the Tractatus
the very picture of simplicity that it was in fact already concerned to challenge; or the
Tractatus’ picture of simplicity is done full justice, but only at the cost of no longer
regarding it as falling within the target of PI §50 and of thereby rendering PI §50 nearly
redundant. Of course, the trivial way out consisting in holding PI §50 to assail a
caricatured version of the Tractatus’ picture of simplicity is hardly more palatable. Our
aim is to steer a path between the Charybdis of an irresolute interpretation of the Tractatus
and the Scylla of a redundant interpretation of the Philosophical Investigations.8
§3. The ultimate concern of PI §50 is none other than the issue underlying the
countenancing of simple objects or elements in the Tractatus: namely, the issue of the
determinacy of sense. In effect, PI §50 is ultimately a reappraisal of the line of reasoning
through which the Tractatus argued for the requirement that “simple signs” (einfache
Zeichen) – i.e. signs designating “proto-elements” (Urelemente) – be possible (TLP 3.23),
on the basis of its prior commitment to the requirement that sense be determinate. PI §50
reopens the question of why the determinacy of sense should have assumed the form of a
requirement in the first place.
It is precisely at the level of this issue that the respective thoughts of Wittgenstein and
Kripke engage one with another. While this is evidently true of Kripke’s study of PI §§ in
6
Two notable exceptions in this respect are Gert (2002), (2010) and Diamond (2001).
Two notable exceptions in this respect are Diamond (2001) and Dolev (2007a), (2007b).
8
This is the aim of any “resolute reading” of Wittgenstein’ work, properly understood: see Conant (2007).
7
4
Wittgenstein on Rules and Private Language, it is no less true, I think, of his critical
discussion of PI §50 in the first lecture of Naming and Necessity. Arguably, a concern for
the false requirements laid by philosophers upon our very ability to mean our words
permeates Kripke’s entire work. In Naming and Necessity, Kripke is concerned with
tracing the false strictures laid upon our very ability to use names to a certain picture of
how their meanings are fixed. His aim is to expose that picture for what it is, a mere
picture, by making room for an alternative one.
At a certain level of generality, the two authors might even be said to concur in their
diagnosis of the modalities along which the plain determinacy of our meanings is turned
into philosophical strictures on our ability to mean what we say, whose tenor ensures that
they cannot be met – at least not effectively met. According to them both, in our effort to
secure the distinction between the standards of sense and their employment, and to make
sure that the former hold fast regardless of what happens to be the case, we are prone:
first, to mistake the logical fixity of the standards of sense for some kind of supra-physical
rigidity (call it the ‘indestructibility’ of the fixed; second, to “predicate of the thing what
lies in the method of representation” (PI §104), thereby turning the standards of sense into
elementary constituents of reality.
Part of the special significance accruing to Kripke’s critique of PI on the matter of the
length of the standard meter is due to the fact that the notion of a metrical standard (i.e.
that of a standard of measure) – such as “the standard meter in Paris” (das Urmeter im
Paris) – is overdetermined in the works of both Kripke and Wittgenstein, in different
albeit related ways.
Like the common non-literal notion of rigidity (one talks of a rule being “rigid”),
Kripke’s notion of “rigidity” involves a logical extension of the original physical notion of
rigidity (one talks of a body being “rigid”, meaning that it cannot be bent or deformed
beyond a certain definite degree). When Kripke introduced his new term of art, the notion
of congruence (i.e. of the equality of length between bodies) had long been shown to
involve two distinct notions of rigidity, at two distinct levels. The question whether a
measuring rod retains its length when transported is one that it is not physically but
logically impossible to settle (that is, settling it makes no sense). It can be settled only by
stipulation: two measuring rods shown to be equal in length by local comparison at a
certain space point are defined as equal in length at a distance (hence as equal in length
simpliciter). Such a convention possesses the rigidity of an arbitrary rule. However, this is
not merely a linguistic convention. For one thing, the concept of congruence (i.e. of
equality of length) is defined by “coordinating” to it a certain physical structure (namely
the two measuring rods shown to be equal by local comparison at a certain space time),
just as the definition of the concept of the unit of length “meter” is defined by
“coordinating” to it the standard meter. For another, what makes that coordinative
definition at once unique (i.e. independent of the path of transportation) and uniquely
practical is a fact, knowable only a posteriori, regarding the behavior of measuring rods as
rigid bodies, namely the fact that
Two measuring rods shown to be equal in length by local comparison at a certain
space point will be found to be equal in length by local comparison at every other
space point, whether they have been transported along the same or different paths.9
As for rigid bodies, they are just “those bodies that constitute the physical part in the
9
Reichenbach (1957) §4 p.16. In the same manner, the coordinative definition through which successive
time intervals are defined as equal is both unique and uniquely practical in virtue of the fact, knowable only
a posteriori, that “all periodic processes, and furthermore inertial motion and the motion of light, lead to the
same measure of time.” (Reichenbach (1957) §17 p.117)
5
coordinative definition of congruence and that by definition do not change their size when
transported”10. That their shape is “unchangeable” is not some fact about them11. For their
shape to be “unchangeable” is for it to be logically rigid. To hold otherwise is to
“predicate of the thing what lies in the method of representation” (PI §104).
One issue that is implicitly addressed by Kripke’s account arises from the fact that the
stipulation that the metal bar chosen as standard stays the same length when transported
stands in need of an important qualification. The length stipulated to stay the same can
only be the corrected length of the metal bar chosen as standard, i.e. its length after
theoretical correction for the action upon it of perturbational influences, including
“universal forces” (i.e. forces deforming all bodies in the same way, independently of
differences in internal resistance to deformation).12 However, while the stipulation that
universal forces should vanish falls short of explaining how the reference of the term
“meter” can be uniquely fixed by means of the coordinative definition,13 the strictly
stronger stipulation that the metal bar should be free from all known physical influences
(universal forces do not count among known forces) makes the fixation of reference
depend upon knowledge. On Kripke’s alternative account, all that is required is some
actual relation, possibly mediate, to the metal bar itself and so to its actual length.14
Crucially, the length stipulated to stay the same is the corrected actual length of the metal
bar.
§4. Wittgenstein apprehends the normativity of sense – as reflected in the “distinction
between the determination of a sense and the employment of a sense” (RFM III §37) – on
the model of the normativity attached to units of measure (like the meter or the yard).
Thinking of the normativity of sense in such terms enables one to do justice to its
autonomy and thereby to its determinacy. What must hold fast in order for so much as a
negative description determinately to engage with reality is best thought of as a unit for
the measure of a determinate magnitude:
“I haven’t stomach-ache” may be compared to the proposition “These apples cost
nothing”. The point is that they don’t cost any money, not that they don’t cost any
snow or any trouble. The zero is the zero point of one scale. And since I can’t be
given any point on the yardstick without being given the yardstick, I can’t be given its
zero point either. “I haven’t got a pain” doesn’t refer to a condition in which there can
be no talk of pain, on the contrary we’re talking about pain. (…) I don’t describe a
state of affairs by mentioning something that has nothing to do with it and stating it
has nothing to do with it. That wouldn’t be a negative description. (PR §82)
If I say I did not dream last night, I must still know where I would have to look for a
dream (i.e. the proposition ‘I dreamt’, applied to this situation can at most be false, it
cannot be nonsense). I express the present situation by a setting – the negative one –
of the signal dial ‘dreams – no dreams’. But in spite of its negative setting I must be
able to distinguish it from other signal dials. I must know that this is the signal dial I
have in my hand. (PR §86)
The determinacy of sense and the determinacy of its reversal through negation are one
and the same. What they require is not the ability to recognize the presence of something
(say, pain), if that is something distinct from the ability to recognize the absence thereof,15
10
Reichenbach (1957) §5 p.22.
Reichenbach (1957) §5 p.20.
12
See Putnam (1975) p.172.
13
See Putnam (1975) p.174, pp.186-191.
14
See Putnam (1975) pp.176-177. See also Putnam (1973) pp.198-204.
15
See PR §86.
11
6
but rather the possession of a ‘paradigm’ (Paradigma) with which to compare reality, akin
to the standard meter in Paris (das Urmeter im Paris).16 In the thoughts that this is red and
that this is not red, the possibility that this be red must show forth, yet not be assumed to
obtain, even in the most shadowy way.17 Arguably units of sense in the Tractatus are
already conceived of as units of measurement. Only, such units (the Tractarian objects) are
yes-no units rather than scales, and they are not the result of stipulation.
In Wittgenstein’s later work, the assimilation of units of sense to units of measurement is,
if anything, more literal. On the one hand, the establishment of a unit of measurement is
literally a rule of grammar, i.e. a rule for the use of a word (such as “red”). On the other
hand, any rule of grammar may be conceived as the specification of a unit of measurement
(such as “the meter”) to the extent that “rules of grammar are arbitrary and are not
arbitrary in the same sense as is the choice of a unit of measurement”. In the sense in
which an ascription of length is answerable to reality (it is ‘correct’ or ‘incorrect’), a rule
of grammar is not. As the specification of a unit of length (Maßeinheit) is not a
specification of length, so the specification of the use of a word is not the specification of
a fact. But in the sense in which the choice of a unit of length is answerable to reality and
suitable to us (it is ‘felicitous’ or ‘infelicitous’, because ‘practical’ or ‘impractical’), a rule
of grammar is.18 The logical ‘rigidity’ attached to the standard meter or to a ruler (or more
generally to a rule of grammar) as a standard is not of a stricter kind than the literal,
physical rigidity that is required of it as a body. Nor does it depend upon the latter. This is
the sense in which “a rule qua rule is detached, it stands as it were alone in its glory”
(RFM VII §3). For all that,
You can’t say: “yes the measuring rod (der Maßstab) measures length in spite of its
corporality (Körperlichkeit); but a measuring stick that had only length would be the
ideal, would be the pure measuring stick”. No, if a body has length, then there can’t
be any length without a body – and even if I understand that in a certain sense only
the length of the measuring rod does the measuring, yet what I put into my pocket is
still the measuring rod – the body and not the length. (BT p.352e.)
The defined length is abstract: it is not maximally unalterable, but logically unalterable.
This does not mean that we have no reasons to keep the standard meter in a vault and “to
manufacture rulers out of ever harder, more unalterable material”. It only means that we
could have reasons to employ elastic rods as our rulers.
§5. Kripke’s positive contention about the standard meter in Paris – namely, that
statement L (“S is one meter long at t0”) is best construed as at once a priori and
contingent – has seemed to fly in the face of Wittgenstein’s insistence that “the
justification inherent in grammar as such doesn’t exist for grammar.”19 It has seemed to
arise from conflating a rule for the use of the words “one meter” with a special use of
these words and from failing to distinguish the sense in which a rule can be turned back on
itself from the sense in which it cannot.20 The very picture of logical necessities as truths
holding in all possible worlds might indeed seem to betray the temptation, against which
Wittgenstein warns his reader, to equate logical necessities with ‘super-rigid’ states of
affairs.21 Now, Kripke does not deny what Wittgenstein asserts, namely that the
establishment of a unit of measurement is a rule for the use of its designation, while an
16
See PR §11; PG §95.
See PG §95.
18
BT p.186e. See also LFM p.249.
19
BT p.185e.
20
See Fogelin (2009) pp.104-108.
21
See Diamond (1991) p.192, p.198.
17
7
ascription of length in terms of this unit makes use of that rule.22 Nor does he assert what
Wittgenstein denies, namely that the stipulative definition of a unit of length, is an
ascription of length.23 But even in the circumstance that the above suspicion should be
funded, it would still not follow that Kripke’s qualms about the pair of remarks he extracts
from PI §50 are at odds with the overall argument of PI §50. Kripke’s cautiousness in
advancing his positive contention24 and his subsequent qualifications of it25 do not extend
to these qualms. Conversely, some at least of Wittgenstein’s sayings about ascriptions of
lengths might bespeak the sort of verificationist strictures criticized by Kripke. Even so,
however, such strictures need not be readable into PI §50.
I shall argue that Kripke’s qualms need not be defused on Wittgensteinian grounds.
Therefore, that Kripke’s qualms cannot be so defused anyway, as I also argue elsewhere,
counts as no objection to Wittgenstein’s overall argument in PI §50. The latter argument
lies outside the compass of this paper. I shall merely indicate its overall shape.
Attempts at rebutting Kripke’s critique of PI §50 on (allegedly) Wittgensteinian grounds
may be sorted into two groups, depending on the kind of diagnosis on which they turn.
According to the first kind of diagnosis, it can only look to us as if the truth of L (“S is one
meter long at t0”) were at once a priori and contingent, to the extent that we unwittingly
oscillate between two ways of apprehending S – namely, as the standard for the unit of
measurement called “meter” (by reference to which any other metal bar is to be assessed
with respect to its length) and as a mere metal bar (which, like any other, can be assessed
with respect to its length) – that are in fact mutually exclusive. Such oscillation tempts us
into thinking that our grammatical knowledge of the features of a system of representation
and our empirical knowledge of facts represented by means of that system are of a nature
to overlap, so that L can be construed in both ways at once. Equating the reference of
“meter” with some abstract object distinct from the metal bar S instead of equating it with
S itself is, on this account, but the other side of the same mistake. The same failure to keep
sight of the distinction between a grammatical feature and a property of an object leads
Kripke to mistake a feature of the use of the word “meter”, now for some accidental
property of the metal bar S, now for the essence of some abstract object distinct from S. As
against the former move, it is objected that S is not found, let alone measured, to be one
meter long. As against the latter move, it is objected that the abstract object allegedly
supplying the reference of “meter” evidently stands in need of, yet conspicuously lacks,
criteria of identity of its own. This diagnosis typically helps itself to the view that the
significance of the qualification entered by C2 is that the assertion of the nonsensicality of
L and ~L alike by C1 should be seen as an expression or even a consequence of the
grammatical truth that L can be seen to convey – or at least to gesture at, in spite or rather
in virtue of its very failure to convey it (due to either its emptiness or its nonsensicality) –
and which, put in the material mode, is none other than the necessity that S be one meter
long at t0. On this account, Kripke’s lapse into nonsense can be traced to a violation of the
grammatical rule which “S must be one meter long at t0” tries to formulate in the material
mode and which we can be said to have laid down in laying down the use of “meter”.
This diagnosis is deeply flawed. The charge that Kripke’s critique of PI §50 rests on a
gross misreading of PI §50 itself rests on a gross misreading of both Kripke’s critique and
PI §50 itself. For one thing, Kripke does not take the point of C1 to be, nor should the
point of C1 be taken to be, the simple point that S cannot be found, let alone measured, to
be one meter long at t0. Kripke knows better than to deny such a point (which is of course
22
See BT p.189e.
See BT p.190e.
24
See NN pp.56-57.
25
See Kripke (2011) pp.304-305.
23
8
correct), just as he knows better than to read it into C1 (whose point he rightly takes to be
the much stronger one that S cannot at all be stated to be one meter long at t0). For another
thing, in eschewing ascribing to Wittgenstein the view that L and ~L contravene to a
grammatical rule, Kripke’s reading of PI §50 is arguably far more consonant with
Wittgenstein’s own view of grammatical elucidation than the above account.
These distortions are explicitly disavowed by the line of response to Kripke’s critique
that turns on the second kind of diagnosis. This second line of response takes issue, in
particular, with the verificationist strictures tacked on by the first on Wittgenstein’s text.
On this alternative diagnosis, no invocation of grammatical rules could establish that
Kripke has unwittingly lapsed into nonsense. Nonsense does not stem from infringing
grammatical rules; nor do grammatical rules set bounds to the realm of sense. That
Kripke’s claim that we have a priori knowledge of the truth of L is nonsense in disguise
can be shown, on this alternative diagnosis, by bringing out the parallelism obtaining
between this claim and the patent nonsense of a boy’s claim to show you how tall he is by
laying his hand on his head (see PI §279). The second line of objection thus stands or falls
with the claim that such a parallelism obtains. Although far more compelling than the first,
it too is unpersuasive. Or so I argue. Be that as it may, this second line of response to
Kripke’s critique, by contrast with the first, only disputes Kripke’s positive contentions; it
does not dispute his qualms. These are thus left intact.
II.
PI §50: Stakes, Background and Problems
§6. The pair of remarks with which Kripke takes issue occur in the course of a lengthy
section whose main point turns on an analogy between the logical impossibility (i.e.
nonsensicality) of attributing (beilegen) either being (Sein) or non-being (Nichtsein) to
elements and the impossibility of stating (aussagen) of the standard meter in Paris (das
Urmeter in Paris) either that it is 1 meter long (es sei 1m lang) or that it is not 1 meter
long (es sei nicht 1 m lang). According to this analogy, being said (not) to be 1 m long is
to being said (not) to be what being the standard meter is to being an element. This
analogy is set against the background of an interrogation, initiated in §46, as to “what lies
behind the idea that names, genuinely speaking, designate what is simple (dass Namen
eigentlich das Einfache bezeichnen).” (PI 46a) In §46, Wittgenstein traces this idea to the
picture exemplified by the presentation (Darstellung) constituting the main bulk of
“Socrates’ Dream”, a well-known passage in Plato's Theaetetus. The closing paragraph of
§46 attests to his having heard in Socrates' Dream a version of his own foregone
Tractarian dream:
Both Russell’s ‘individuals’ and my ‘objects’ (Tractatus Logico-Philosophicus) were
such primary elements.
Thus, at stake in PI §§46-50 is the Tractatus view of simplicity.
The mode of criticism deployed in §48 is the same as the one that was deployed in §226.
Accordingly, it is called in retrospect “the method of §2”. The language-game introduced
in §48 stands to the presentation (Darstellung) from Plato's Theaetetus as the languagegame introduced in §2 stands to the presentation from Augustine's Confessions on which
the book opens: it is one for which the presentation holds (gilt). Just as the excerpt from
Augustine's Confessions was meant to exemplify the picture (Bild) of (the essence of)
human language in which a certain idea (Idee) about language is rooted – namely, the idea
that to every word corresponds, as its meaning, the object for which that word deputizes –
26
On this parallel, see Gert (2002) p.58; Stern (2004) pp.10-21; Jolley (2010) p.115.
9
so in §46 the excerpt from Plato’s Theaetetus is meant to exemplify the picture of naming
in which the idea (Bewandtnis) that “names, genuinely speaking, designate what is
simple” is rooted. And just as §2 cashes out a certain “primitive conception (Vorstellung)
of the way language functions” in terms of “the conception (Vorstellung) of a language
more primitive than ours.” (PI §2a), so does §48 with respect to the conception of naming
that emerges from Socrates’ Dream. A philosophical concept of naming is criticized on
account not of its falsity but of the primitiveness and the parochialism of the languagegame and the form of life to which it does prove appropriate. In between §46 and §48,
Wittgenstein interpolates a lengthy section (§47) that paves the way for the consideration
of language-game (48) by showing both that the ontological question as to what being
simple comes to cannot be severed from the logical question as to what counting as simple
comes to, and that the latter only makes sense relative to a certain context.
The language-game introduced in §48 is characterized thus:
The language serves to present (darzustellen) combinations of colored squares on a
surface. The squares form a complex like a chessboard. There are red, green, white
and black squares. The words of the language are (correspondingly (entsprechend))
“R”, “G”, “W”, “B”, and a sentence is a series of these words. They describe
(beschreiben) an arrangement (eine Zusammenstellung) of squares in the order:
And so for instance the sentence "RRBGGGRWW" describes an arrangement of this
sort:
(PI §48)
Wittgenstein goes on to observe that, in the context of such a language-game, a “sentence
is a complex of names, to which corresponds (entspricht) a complex of elements” and that
one could hardly find something that more naturally deserved to be called the “simple”
(das Einfache) than the colored squares making such elements. This evidently parallels the
claim that, in the context of language-game (2), one could hardly find something that more
naturally deserved to be called the “meaning” of a word than the object for which it
stands. Equipped with the language-game of §48, Wittgenstein can then proceed to
address in section §49 the question of what it means to say, as the presentation from
Plato's Theaetetus does, that “we cannot give an account of (that is, describe) elements,
but only name them” (dass wir diese Elemente nicht erklären (d.h. beschreiben) sondern
nur benennen können) (PI §49a). The question is raised and answered with reference to,
and in the terms of, language-game (48).
§7. We can now, at last, turn to PI §50 itself. I quote it in full:
Now, what does it mean to state, of the elements (Elemente), that we can attribute
(beilegen) neither being (Sein) nor non-being (Nichtsein) to them? — One might say:
if everything that we call “being” and “non-being” consists in the existence and nonexistence of connections between the elements (im Bestehen und Nichtbestehen von
Verbindungen zwischen den Elementen), then it makes no sense to talk (sprechen) of
an element’s being (non-being); just as when everything we call “destruction”
(“Zerstören”) lies in the separation of elements (in der Trennung von Elementen
liegt), it makes no sense to speak (reden) of the destruction of an element.
One would, however, like to say: being cannot be attributed to an element, for if it
were not, one could not even name it and so one could state nothing at all of it. — But
let us consider an analogous case! There is one thing of which one can state neither
that it is one meter long, nor that it is not one meter long, and that is the standard
meter in Paris (das Urmeter in Paris). — But this is, of course, not to ascribe any
10
extraordinary property to it (nicht irgend eine merkwürdige Eigenschaft
zugeschrieben), but only to mark its peculiar role in the game of measuring by means
of the meter-rule. — Let us imagine samples of color being preserved in Paris like the
standard meter. We define: “sepia” means (heiße) the color of the standard sepia (UrSepia) which is there kept hermetically sealed. Then it will make no sense to state of
this sample either that it has this color or that it does not.
We can put it like this: This sample (Muster) is an instrument (Instrument) of the
language, by means of which we make color-statements (Farbaussagen). In this game
(Spiel) it is not something that is represented, but a means of representation (nicht
Dargestelltes, sondern Mittel der Darstellung). — And just this holds of an element
in language-game (48) when we name it by pronouncing (aussprechen) the word “R”:
we have thereby given to this thing a role in our language-game [Sprachspiel]; it is
now a means of representation (Mittel der Darstellung). And to say “If it were not, it
could have no name” is to say as much and as little as: if there were not this thing, we
could not use it in our game. — What, on the face of it (scheinbar), there must be, is
part of the language. It is a paradigm (ein Paradigma) in our game; something with
which comparison is made. And you can call it to make an important observation to
observe this; still, it is with our language-game (unser Sprachspiel) – with our method
of representation (unsere Darstellungsweise) — that such an observation has to do.
(PI §50)
The standard meter is invoked in the course of an attempt at dislodging a certain picture
of simplicity, one that Wittgenstein takes to inform both Socrates’ Dream and the
Tractatus. The fascination exerted by this picture underlies the reluctance with which the
first try at a deflationary account of the impossibility of attributing (beilegen) either being
(Sein) or non-being (Nichtsein) to elements is met.27 The argument broached at the
beginning of §50b is meant to ward off the suggestion that the impossibility of attributing
either being or non-being to elements results from a stipulation as to what to call being
(Sein) and non-being (Nichtsein) and to that extent is a mere reflection of our ways of
talking. Drawing from neighboring sections, we may rephrase the reluctance to which this
argument lends support as follows: in the face of the deflationary account, we are inclined
to insist that the impossibility of attributing combinatorial being to elements is a reflection
of the fact that they “exist in their own right” (PI §46, §58). They have being in some
other and more fundamental sense – call it “being in virtue of one’s own essence”. In a
more Tractarian mood, we might say that what shows forth in some sign being used as a
name, i.e. as a symbol for an element, cannot be said. But, one is inclined to think, what
thus shows forth is precisely what “A is” (where A is the name of an element) tries and
fails to say (see PI §58c). It is therefore as if “A is”, far from not making sense, only made
too much sense. Note that nothing in these last, Tractarian (or pseudo-Tractarian)
formulations implies that what “A is” tries and fails to say, i.e. what shows forth in ‘A’
being a name, is that A is an object, let alone that A is.
But why this should be so is a matter on which §50b says very little. All that is said is
that if A did not exist, then it would not be so much as nameable, so that it could not be
spoken of in the first place. From this, together with the premise (left implicit) that it
makes sense to attribute being to A only if it makes sense to attribute non-being to A (i.e.
to deny being from A), the conclusion that it makes no sense to attribute being to A is
supposed to follow. The details of the underlying argument must be filled in, and the
argument itself expanded. If what shows forth in “A” being a name, and which “A is” tries
and fails to say, could fail to show forth, then a situation would be possible in which A
would not be there to be named, so that we could not so much as speak of it at all. On the
27
See Jolley (2010) p.111, p.119.
11
assumption, suggested by the combinatorial account of being and nonbeing, that names
are the end-points of analysis, the argument calls for being expanded as follows. If names
lie at the limits of all analysis, then it is perforce of elements that we always speak
ultimately. If so, to envision a situation in which we cannot so much as speak of A is to
envision a situation in which there are indefinitely many complex things that cannot be
stated to be or not to be. But for such a situation to be conceivable, it would have to be
conceivable that our very capacity to make sense might fail us. And that is absurd.
Therefore, what “A is” tries and fails to say, cannot fail to show forth. Should this last
claim turn out to be equivalent to the claim that A must “exist in its own right” or “with
necessity”, then the argument will have established, by the same token, this last claim.28
Construed along the lines, the argument broached at the beginning of §50b assumes the
shape of a “transcendental argument”: that what “A is” tries and fails to say cannot fail to
show forth is a condition of possibility of our ability to make sense. Of course, even so
fleshed out, the argument is still schematic, as the notions of situation and possibility it
invokes are conspicuously ambiguous.29 As we shall see, one of the virtues of Kripke’s
thought in this regard is that it can help to bring the ambiguity of these notions into light.
It is worth emphasizing that to the extent that this argument can be said to argue in favor
of the necessary existence of elements, it must be recognized to do so on the basis of a
prior argument in favor of their simplicity, rather than the other way around.30 The
argument is also worth comparing to the argument on the basis of which ascriptions of
existence to individual objects have been reckoned incoherent and analyzed out as
ascriptions of the second-level concept of existence to first-level concepts. If we say e.g.
that satellites of Mars exist, the argument runs,
Even if we were assured that Mars had some satellites, the question would arise, if
existence were a property, whether all of Mars’s satellites had the property, or only
some of them, whereas such a question is patently senseless; in fact the proposition
that there are satellites of Mars embodies all that we wished to assert in asserting such
satellites to exist.31
That is to say, “ξ exists” is not a first-level predicate expressing a property of objects, but
a second-level predicate expressing a property of first-level concepts (as for Frege) or a
property of propositional functions (as for Russell)32. On pain of there being room for
28
As will become clear, I doubt that the antecedent of this conditional can be ascribed to the Tractatus.
See Proops (2007); Zalabardo (2012).
30
By contrast, the argument rehearsed in §39, which is taken from Russell, argues in favor of the simplicity
of elements through arguing through their necessary existence: “But why does it occur to one to want to
make precisely this word into a name, when it evidently is not a name? – That is just the reason. For one is
tempted to make an objection against what is ordinarily called a name. It can be put like this: a name ought
really to signify a simple. And for this one might perhaps give the following reasons: The word “Nothung”,
say, is a proper name in the ordinary sense. The sword Nothung consists of parts combined in a particular
way. If they are combined differently Nothung does not exist. But it is clear that the sentence “Nothung has
a sharp blade” makes sense whether Nothung is still whole or is broken up. But if “Nothung” is the name of
an object, this object no longer exists when Nothung is broken in pieces; and as no object would then
correspond to the name it would have no meaning. But then the sentence “Nothung has a sharp blade” would
contain a word that had no meaning, and hence the sentence would be nonsense. But it does make sense; so
there must always be something corresponding to the words of which it consists. So the word “Nothung”
must disappear when the sense is analyzed and its place be taken by words that name simples. It will be
reasonable to call these words the real names.” (PI §39) As we shall see, there is no reason to read this
argument – “the Empty Name argument” (see Zalabardo (2012) p.119) – back into the Tractatus. But nor is
there, anyway, any reason to take sections §§39-40 to be directed against the Tractatus view of simplicity.
On both counts, I entirely concur with Zalabardo (2012).
31
Dummett (1993) pp.277-278.
32
See Russell (1918) pp.232-234.
29
12
quantifying over non-existent objects, “ξ exists” must be none other than the second-level
predicate “there is”, i.e. the so-called “existential quantifier”.33
One is drawn to the same general conclusion if one attends to the old riddle of non-being
arising in connection with negative singular existential statements of the form “A is not”.
It would seem that such statements are essentially self-defeating, insofar as we cannot so
much as meaningfully assert that “A is not” unless ‘A’ has a reference (i.e. unless A is, in
some sense or other). The existential case is a limiting one: the point is that if A were not,
then we should not be talking about anything when using ‘A’, so that even to say that A is
not would be nonsense.34
By itself, however, this last observation does not imply the radical and general
conclusion that it is strictly and equally nonsensical either to ascribe existence to objects
or to deny it of them. Rather, its limited upshot is that “A is not” is either self-defeating (if
true) or redundant (if its negation is true), while conversely “A is” is either redundant (if
true) or self-defeating (if its negation is true). One might be tempted to say that where ‘A’
is a name, what “A is” would say, if only that could be said, is true (as Russell sometimes
suggests); or even that “A is” is just as self-evidently and as universally true as a
statement of self-identity like “A is A” (as Frege sometimes maintains35). Such claims
support a “redundancy view of existence” (according to which existence, like self-identity,
is a property that holds of every object) that is strictly speaking incompatible with the
view that existence is a property of property. Whether Kant’s famous contention that
existence is not a real predicate – i.e. that it is no additional character of the concept of the
object (say, this particular bird) stated to exist, on a par with its other characters (like e.g.
flying) – but rather the absolute position of the object in question (with all its predicates),
prefigures one view or the other (if any) is unclear.
The converse argument, by contrast, carries through. From the general thesis that
existence is a second-level concept, the claim does follow, that the affirmative existential
“A is” and the negative existential “A is not” are strictly and equally nonsensical. But to
arrive at the conclusion that “A is” (where A is a name) is nonsensical, calling attention to
the pair of puzzles attending singular existentials is not enough. Additional premises are
required: that only what is simple can be named; that only what can be stated can be stated
to be; that only what is not simple can be stated. These are premises that Russell and the
early Wittgenstein can be said to share – if only nominally (a symptom of the skin-deep
character of their convergence is that Russell endorses, while the early Wittgenstein
rejects, the assimilation of facts and complexes).
In the light of these considerations, the first thing to note about the opening argument of
§50b is that it does not give prominence to the paradox of negative singular existentials.
The second thing to note about this argument is that, in stark contrast to the deflationary
claim on which §50a opens and the less specific claim that “A is” and “A is not” are
strictly and equally nonsensical, both of which take the form of a joint denial securing a
strict parity between being and non-being, it has imparity built into it. Part of the objection
to the deflationary claim is precisely that it treats “A is” and “A is not” as if they stood on
a par. The Tractatus holds on to the parity more consistently than Frege and Russell ever
did. Its stance remains ambiguous, however – at least when taken at face value. It is well
captured by this later remark:
When one says that substance is undestroyable, what one means, is that it is senseless
in any context to talk – whether affirming or denying – of ‘the destroying of a
substance’. (PB §95)
33
See Quine (1948), Dummett (1993).
See Quine (1948) p.2.
35
On this tension in Frege, see Mendelsohn (2005) Chapter 7.
34
13
In response to which one feels inclined to ask: why say it is “undestroyable” (rather than,
say, “irrefrangible”, or “inedible”, or what not) then? What makes this meta-linguistic
denial more relevant than any other? This is an issue to which we shall have more than
one occasion to revert.
The last tract of §50 is clearly concerned with disarming the above argument. It reaches
the diagnosis that the appearance that there must be a certain thing – say, that there must
be this, to which “A” refers – is but an artifact of language. Finally, it warns against the
temptation to take such an artifact to be anything else than an artifact of our language.
What is altogether unclear is the role played in all that by the invocation of the standard
meter.36 On the surface, the analogy at play is one between the nonsensicality of
attributing (beilegen) either being (Sein) or non-being (Nichtsein) to elements and the
nonsensicality of stating (aussagen) of the standard meter in Paris (das Urmeter in Paris)
either that it is 1 meter long (es sei 1m lang) or that it is not 1 meter long (es sei nicht 1 m
lang).37 But this leaves room for more than one way of construing the function of the
analogy within §50.38 And what function is ascribed to it has a direct bearing on one's
understanding of the deflationary intent of §50. By way of consequence, it has a direct
bearing on one’s understanding of the kind of deflation secured by rephrasing logical
necessities in grammatical terms.39
§8. I now turn to the main tenets of reading of the “standard reading” of PI §5040. Let me
rehearse the two claims upon which Kripke fastens:
C1
There is one thing of which it can be stated neither that it is 1 m long nor
that it is not 1 m long, namely the standard meter S kept in Paris.
C2
To assert C1 is not to ascribe to the standard meter S any extraordinary
property, but merely to register its unique role in the language-game of
measuring in meters.
On the standard reading of PI §50, the first claim can be said to be endorsed without
qualification by Wittgenstein provided it be seen in light of the second.41 On this reading,
36
As we shall see, it is not even clear that the standard meter constitutes itself the second term of the
analogy. See section 3.1 below.
37
At bottom, however, the analogy at work proves to be one that involves existence on both sides. See
section 3.1 below.
38
See note 42 below.
39
The diagnosis advanced in §50 resonates with the genealogy of the pseudo-problems of philosophy
countenanced in §104: “We predicate of the thing what lies in the method of representation (in der
Darstellungsweise). Impressed by the possibility of a comparison, we take it for the perception of a situation
of the highest generality.” That the deflationary point made in §50 neatly illustrates the deflationary benefit
of rephrasing logical necessities in grammatical terms is clear from these passages: “The difficulty arises in
all such cases from mixing [die Vermischung] 'is' and 'is called'. The connection [Verbindung] which has to
be, not a causal or experiential one, but rather a much stricter and harder one, so rigid even that the one thing
somehow already is the other, is always a connection in grammar [eine Verbindung in der Grammatik].”
(BGM §§127-128)
40
It bears emphasizing that this designation is not in line with the homonymous designation by which socalled “resolute readings” of Wittgenstein (early and late) designate the kind of reading that they charge with
being “irresolute”. In fact, the distinction drawn in this chapter between “standard readings” and “nonstandard readings” of PI §50 is orthogonal to the distinction marked by “resolute readings”.
41
As Kelly Jolley puts it, “Wittgenstein is speaking in his own assertive voice when he says what he says
about the standard meter.” (Jolley (2010) p.107) At this level generality, the standard reading can be
ascribed to the following commentators: Avital (2008); Baker & Hacker (1980a), (1980b);
Bouveresse (2006); Fogelin (1995), (2009); Jolley (2010); Loomis (1999); Malcolm (1995); Pollock (2004);
Dolev (2007a). It should be noted, however, that while they ascribe C1 to Wittgenstein without qualification
(or without any other qualification than that it should be construed in the light of C2), Dolev and Jolley,
14
the reason why C2 is called for is that the deflationary character of C1 is bound to elude us
as long as we are in the grip of the picture that C1 means to dislodge. By showing C1 for
the deflationary point that it is, C2 definitively dissipates the air of paradox that C1 is
initially bound to assume in our eyes. The point of the analogy is to expose the
nonsensicality of the metaphysically loaded claim that neither being nor non-being can be
attributed to an element by contrasting it with a claim which, although counterpart to the
first, makes plain sense, presumably because the words it employs are plainly at home in
the context in which it is uttered, whereas before they were done violence to.42 C1 makes
plain sense insofar as it merely lends expression to the role played by the standard meter
as long as it serves as the standard meter. On the standard reading, where the Tractatus
went astray was in failing to realize that the impossibility of stating of an element either
that it is or that it is not did not reflect its essence but only the role played by it – that is to
say, the role conferred to it. In a nutshell, it mistook samples for simples, i.e. for
necessarily existing objects.
The standard reading passes over in silence a number of exegetical problems that a
reading of PI §50 should address. Perhaps the most acute of these has to do with its
account of the critical bearing of PI §50 on the Tractatus’ view of simplicity. But the
standard reading is also beset with problems of its own.
Firstly, any reading of PI §50 is confronted with the difficulty of making sense of the
closing paragraph of §46, where Wittgenstein declares that Russell’s “individuals” and the
“objects” of the Tractatus equally count as primitive elements (Urelemente) in the sense
of Socrates’ Dream. On the face of it, aligning Russellian individuals on Tractarian objects
flies in the face of the Tractatus’ evident disavowal of Russell’s semantic atomism.43
Secondly, insofar as it takes for granted a combinatorial conception of being and nonbeing, the argument of §50, on the face of it, begs the question. In effect, the reluctance
with which the first deflationary attempt of §50 is met can be read as a reluctance to
concede that the meaning of “being” is simply exhausted by its combinatorial meaning.
Surely such reluctance cannot be dismissed without a second thought. That the existence
of anything should consist in the obtaining of a combination or a complex, that is to say in
the obtaining of something else, is no trivial assumption. Not only is this assumption not
incompatible as such with an analysis of existential statements as ascribing existence to, or
denying it of, complex subjects, but it might seem germane to the latter analysis insofar as
it is likewise committed to the assumption that existential statements are complex.
Accordingly, some philosophers have imputed the puzzles allegedly posed by singular
unlike the rest of these commentators, do not take Wittgenstein to endorse C1 “without qualification” if that
means “without any consideration of context”. According to both of them, Wittgenstein could not endorse
C1 as it stands if C1 did not encapsulate an implicit restriction to the preparatory stage of introducing the
word “meter”.
42
According to one version of the standard reading (hereafter “S1”), C1 is the result of the transposition of
the metaphysically loaded claim about elements into a register in which it ceases to be so loaded. C1 paves
the way for a reinterpretation of that claim, which C2 then shows how to carry out (see e.g. Baker &
Hacker (1980a), (1980b); Bouveresse (2006)). According to another version (hereafter “S2”), C1 is the result
of applying the “method of §2”, rather than a method of transposition, to the metaphysical claim about
elements. On this reading, §50 carries further the procedure initiated in §48. Thus, by “bring[ing] words
back from their metaphysical to their everyday use” (PI §116) – that is to say, by redeeming a certain stretch
of discourse by pointing “in what special circumstances [it] is actually used”, “it makes sense” (PI §117) –
the analogy shows a contrario that in the metaphysical claim “language goes on holiday” (PI §38).
43
See Ishiguro (1969); Kenny (1974) p.6; Anscombe (2011) p.182. Anscombe writes: “There is certainly a
problem of interpretation here. I don't know if anyone has tacked it successfully.” (Anscombe (2011) p.182)
The difficulty is all the more acute as Socrates' Dream is anyway not clearly susceptible to the Russellian
reading. For one thing, as Anscombe points out, “the passage in Plato does not speak of the primary
elements as 'given'.” (Anscombe (2011) p.182)
15
denials of existence to just that assumption, arguing that it signals a failure to take the
proper measure of Kant’s insight that existence is not a real predicate but the absolute
position of an object (with all its predicates).44 By discarding the assumption that singular
denials are complex, they were able to argue that the rejection of the existence of A is
nothing over and above the rejection of A itself, and so does not require A to refer.
Thirdly, the analogy raises at least two difficulties, both of which are elided by the
standard reading. First, how the analogy is supposed to have the intended import is not
clear. For the “case” with which the analogy is drawn seems most unrepresentative at first.
What is more, no grounds, apart from the analogy itself, have been adduced so far for
seeing it otherwise. Second, at first glance, the analogy at best limps and at worse trades
upon equivocation. For, on the one hand, to attribute or to deny being-1-meter-long is not
to attribute or to deny any existence whatsoever. On the other hand, to attribute or to deny
existence is not to attribute or to deny any first-level property whatsoever, or at least not a
first-level property like any other. Thus, either the analogy limps, or else it equivocates,
construing “to be”, now as predication, now as existence. To this it might be objected that
the analogy is really between two equally unrepresentative, because equally redundant,
first-level properties: those of self-identity and existence. But this objection, although it
encapsulates a genuine insight, is itself vulnerable to to the further objection that selfidentity and existence part company in modal contexts, as there is reason to “assume that
something is self-identical even with respect to counterfactual situations where it would
not exist”45.
Fourthly, there is an evident (if seldom noticed) obstacle to regarding C1, with the
standard reading, as a consequence of the fact that “meter” is stipulated to mean the same
thing as “the length of S at t0”. For if “meter” is introduced as synonymous with a
description, and not just by means of a description, then it can hardly be said to be
indefinable. But if C1 does not reflect on the simplicity of the unit of measure designated
by “meter”, then the analogy carries less conviction.
Finally, there is anyway something disturbing about ascribing C1 to Wittgenstein, given
the overall drift of these sections. For Wittgenstein is emphatic that there is something
mystifying in the very form of the claim that elements can only be named. And C1 is cast
in the same form as this claim. In general, no matter how the Tractarian claim that “what
shows forth cannot be said” (TLP 4.1212) may have to be construed in the end, it is
certainly the case that “the Investigations insist that it is an error to think that there is
something that can’t be said.”46
An appreciation of the force of this last point has prompted a diametrically opposite
reading of PI §50, according to which Wittgenstein, far from endorsing C1, endorses its
negation in §50.47 On this alternative reading, the analogy serves the purpose of exposing
a certain stretch of discourse as nonsensical, not by adducing the “special circumstances”
in which it would actually have made sense, as the standard reading contends, but on the
contrary by adducing a stretch of discourse which, although or rather because it is strictly
analogous to it, is patently nonsensical48.
However, in recoiling from the standard reading, this reading leaves unchallenged what
is perhaps its single most damaging assumption: namely, the assumption that such trivial
things as standards are most unlikely to give rise, just by themselves, to metaphysically
inflated claims. In effect, on this alternative reading, Wittgenstein exposes the
44
E.g. Brentano. On Brentano’s account, see Prior (1967) p.143.
Kripke RE p.38.
46
Anscombe (2011) p.192.
47
See Gert (2002), (2010).
48
This is the method of criticism thematized in PI §524.
45
16
nonsensicality of C1 by helping himself to “an analogous discussion carried on in terms of
objects of a more familiar and undisputed type (standards).”49
But the assumption that the nature of metrical standards is familiar to us and therefore
undisputed is directly belied by a claim which Wittgenstein is repeatedly reported to have
made, to the effect that the relation between Platonic Forms and the things which partake
of them is best construed on the model of the relation between the canonical standard for a
unit of measure (such as the standard meter in Paris or the standard pound) and the
corresponding non-canonical standards or samples (such as meter-rules or poundweights).50 Surely Wittgenstein’s point is not that the idiom surrounding Platonic Forms
turns out to be at home in ordinary talk about standards, but rather that it was a
sublimation of that talk in the first place. Ordinary standards lent themselves to the
elaboration of the notion of Form. And they did so in virtue of their triviality, not despite
it. Platonic Forms are standards, in the very sense in which ordinary standards are. They
supply an elucidation of this sense. As for the assumption that the Tractatus was mute on
metrical standards,51 it cannot be maintained in the face of the fact that the Tractatus gives
them pride of place by conceiving the normativity of propositions in terms of the
normativity pertaining to ungraduated standard in use. There is reason to think that the
Tractatus’ picture of simplicity is already shaped by a certain picture of the simplicity
displayed by standards. It is no accident that the very designation (in German) of the
standard meter (“das Urmeter”) should echo back the designations of both Tractarian
primitive elements (“Urelemente”, “proto-elements”, as one might call them) and
Tractarian proto-types (“Urbilder”).
III.
Tractarian Simplicity
§9. On the face of things, there is no way to make sense of the closing paragraph of §46.
The difficulty does not arise from any discrepancy between the use to which Wittgenstein
puts Socrates’ Dream and Plato’s intentions. On the contrary, the use to which
Wittgenstein puts it seems entirely congruent with Plato's intentions, given that already in
the Theaetetus Socrates’ Dream is deliberately worded so as to remain in itself
indeterminate and to make room for a variety of distinct interpretations52. The difficulty,
rather, is that it is far from clear that interpreting the Dream’s elements as Russellian
individuals is compatible with interpreting them as Tractarian objects, let alone as Platonic
forms.
In the excerpt quoted by Wittgenstein in §46, a combinatorial account of being and notbeing is shown to cohere with an account of the essence of speech whose cornerstone is a
contrast between the articulatedness that proves to be equally intrinsic to what is stated
and to the stating of it and the inarticulatedness of the elements into which what is stated
resolves. Wittgenstein construes the claim that elements (Urelemente) cannot be described
but only named, not as the claim that they are such that nothing can be stated of them (i.e.
that they cannot be spoken about, and in that sense described), but as the claim that they
cannot be stated (i.e. that they cannot be spoken themselves) but only mentioned (i.e.
49
Gert (2002) p.51. This view is of a piece with the view, also espoused by Gert, that C1 is “obviously
false”, its negation, ~C1, obviously true (Gert (2010) p.140). For an apt criticism of the latter view, see the
last section of Jolley (2010), pp.131-139.
50
See Geach (1956) p.74; Bluck (1957) p.115.
51
See e.g. Jolley (2010) p.118.
52
Burnyeat (1990) p.136.
17
spoken of, described externally)53. Elements are what everything else that can be affirmed
or denied, what everything else that can be thought to be or not to be, ultimately consists
of. They are what everything else that can be articulated in speech or thought ultimately
articulates into. Lying at the boundary where articulatedness comes to an end, they
themselves cannot be articulated. As they do not admit of internal description, they do not
admit of definition either. And so to say that they lie at the boundary where articulatedness
comes to an end is to say that they lie at the boundary where analysis comes to an end. If
for something to be (or not to be) so and so, or for something to be (or not to be)
simpliciter, is for some combination of elements to obtain (or not to obtain), to be (or not
to be) the case, then not only does it make no sense to say of an element that it is such as
to be (or not to be) so and so, but it also does not make sense either to say of something
that it is (is not) an element (the concept of “being an element” is not a genuine concept)
or to say of an element that it is simpliciter (i.e. exists) – let alone that it is not simpliciter
(i.e. does not exist).54 (In Russell, the last point becomes the claim that there is simply no
first-level existence predicate, as it is only of propositional functions that existence can be
asserted or denied.)55 Finally, as only what is articulated can be contradicted, it is one and
the same thing to say of elements that they can only be named and to say of their names
that they cannot be negated56.
Socrates’ Dream can be brought in closer alignment with the Tractatus. Thus, on Ryle’s
reading, in addition to claiming that what can be named cannot be stated but only
mentioned, the Dream makes the converse and specifically Tractarian claim that what can
be stated, i.e. articulated into elements, cannot be named but only described. According to
Ryle, the categorial distinction between naming and stating was first rendered intelligible
by Wittgenstein in the Tractatus, in response to troubles that both Frege and Russell had
come up against. But it was already made vivid by Plato in places, including the passage
known as Socrates’ Dream57. And Plato's model of letters and syllables, if properly
construed (namely as a phonetic model) supplies the most perspicuous of models to
convey the insight from Frege that paved the way for the Tractatus' breakthrough:
The phonetic model of letters and syllables would be an almost perfect models by
means of which to express Frege's difficult but crucial point that the unitary
something that is said in a sentence or the unitary sense that it expresses is not an
assemblage of detachable sense atoms, that is, of parts enjoying separate existence
and separate thinkability, and yet that one truth or falsehood may have discernible,
countable, and classifiable similarities to and dissimilarities from other truths and
falsehoods. Word meanings or concepts are not proposition components but
propositional differences. They are distinguishables, not detachables; abstractables,
not extractables – as are the audible contributions made to the voiced monosyllable
53
See PG p.208: “ 'In a certain sense, an object cannot be described.’ (So too Plato: ‘You can’t give an
account of one but only name it.’) Here ‘object’ means 'reference to a not further definable word’, and
‘description’ or ‘explanation’ really means ‘definition’. For of course it isn't denied that the object can be
‘described from outside’, that properties can be ascribed to it and so on.” See Burnyeat (1990) p.150-151.
54
For a Tractarian counterpart to this point, see Sullivan (2004) p.32-33: “There is nothing, except itself, in
whose being so an elementary fact consists. So to talk of the constituents of an elementary fact cannot be to
allude to anything's being so. It is inviting, then, to say that an object is not anything that is so, or is the case;
it just is. But even to say that it is would seemingly be to say that something is so, and thus the invitation is
best declined.”
55
See Russell (1956) p.328: “An important consequence of the theory of descriptions is that it is
meaningless to say ‘A exists’ unless ‘A’ is (or stands for) a phrase of the form ‘the so-and-so’. If the so-andso exists, and x is so-and-so, to say ‘x exists’ is nonsense. Existence, in the sense in which it is ascribed to
single entities, is thus removed altogether from the list of fundamentals.”
56
See Ryle (1960) p.445.
57
Ryle (1960) p.436, pp.442-443; (1990) p.446.
18
“box” by the consonants “b” and “x.”58
While the spoken monosyllable “box” differs audibly in one respect from the spoken
monosyllable “cox”, the audible difference is not a matter of the two monosyllables being
made up out of different separately pronounceable noises, in contrast to the written
difference between the written monosyllables “box” and “cox”, which is a matter of their
being made up out of different separately inscribable letters. Such separately inscribable
characters as “b” and “x” simply do not stand for separately pronounceable noises.59Just
as letters do not stand for atoms of noise, Tractarian names do not stand for atoms of
sense.60 A striking implication of Ryle's genealogy of the Tractatus' central achievement is
that Tractarian names are to be compared to Fregean functional expressions rather than to
Fregean names61. Tractarian elements are patterns rather than atoms of sense. To
understand that the articulatedness through which alone a proposition can articulate a
thought is that of a certain fact, and not simply that of a complex, is to understand that the
articulatedness of a proposition is no form of compositeness62. If the thought expressed by
a statement is to engage with the world, it needs at once to be independent from, and
internally related, to what is the case if it is true. Now, “both needs are met, in part, by the
objects: even if one thinks things to be a way they are not, it is still these things one thinks
to be that way. For the rest, those needs are met by the notion of the form of thought: the
way these things are thought to be (…) is a way those things could be.”63 On the present
reading, the Dream's notion of an element already involves the relevant notion of form and
so meets the second need as well, just as the Tractarian notion of an element does.64
The problem is that reading Socrates’ Dream along these lines makes it unintelligible that
Wittgenstein should mention Russell’s individuals as examples of elements in the sense of
Socrates’ Dream. For Russell keeps conceiving all semantic complexity as compositional
and semantic units as atoms of sense. It is true that in The Philosophy of Logical Atomism,
taking up the Tractarian contrast between names and propositions, he insists that facts
cannot be named65 and conversely particulars cannot be described66. Yet he still maintains,
both that “propositions are complex symbols, and the fact they stand for are complex”,67
and that “in order to understand a name for a particular, the only thing necessary is to be
acquainted with that particular”68.
There is a converse difficulty. There are at least two ways in which PI §50 may be read
as mounting a criticism against Russell's logical atomism, the second of which constitutes
a criticism of Russell's claim that individuals can only be named. But the former criticism
cannot count as a criticism of the Tractarian concept of an object, for the simple reason
that it constitutes, on the contrary, one of its motivations. As to the latter criticism, it is
precisely one to which the Tractarian concept of an object does not seem to be vulnerable.
58
Ryle (1960) pp.435-436.
Ryle (1960) p.435. See also Ryle (1990) p.42.
60
Ryle (1960) p.438.
61
On this point, see also Gandon (2002).
62
See Ryle (1990) p.42.
63
Sullivan (2004) p.33.
64
Ryle seems to hold the simplicity of Platonic Forms to be all too crude in comparison (see e.g. Ryle
(1990) pp.44-45). In reading “self-predications” as expressions of an attempt to convey the unadulterated
exemplariness displayed by both Platonic Forms and Tractarian objects (see Wittgenstein PO p.199),
Wittgenstein seems to suggest otherwise, especially as such a reading coheres with his proposal to construe
Platonic Forms as canonical metrical standards, a proposal partly warranted by the fact that the latter equally
invite “self-predications”. On the last point, see Geach (1956) p.74, pp.81-82.
65
Russell (1918) pp.187-188.
66
Russell (1918) p.200.
67
Russell (1918) p.195.
68
Russell (1918) p.202.
59
19
Or so shall I contend, successively, in the next two sections.
§10. A main bone of contention between Russell and the early Wittgenstein concerns the
nature of the relation between logic and analysis. The first criticism is directed against
Russell’s project of ensuring that logic be a priori amenable to the findings of analysis.
For Russell, logic consists in some completely general propositions in which only logical
forms are mentioned. The main task of philosophy is accordingly to set up an inventory of
logical forms and to establish their applicability. For Wittgenstein, by contrast, as the
possibility of making sense need not and cannot await analysis, the task of philosophy
need not and cannot be so conceived.69 It cannot be incumbent upon philosophy to answer
questions that it is at once superfluous and impossible that it should answer.70 In particular,
it cannot be incumbent upon it that it should arrange for the application of logic.
If we needed to know the forms of elementary propositions and those of the names
comprising them, then the requirement that every proposition be resolvable into a truthfunction of elementary propositions – which is none other than the requirement that
analysis be possible – could fail to be met. What we cannot know a priori, prior to
analysis, namely the forms of elementary propositions and those of the names comprising
them, we need not know either. Conversely, what we need know prior to analysis, namely
the syntactical treatment of the signs comprising our ordinary propositions, including the
syntactical treatment of some as (if they were) primitive signs, we can know anyway,
since for a sign employed in ordinary propositions to call for being treated as (if it were) a
primitive sign just is for it so to behave (or, more accurately, for it not to behave
otherwise).
While it clearly foreshadows PI §50, the following passage from Wittgenstein’s 1935
Cambridge Lectures elaborates upon this early dissent over the relation between logic and
analysis:
We say of the word “yellow” that if it is to have meaning there must be something
yellow somewhere. But why this “must”? Could not everything yellow have been
destroyed? Suppose you learned the names of colors from a chart which correlated
colored patches with certain words like “yellow”, “green”, etc. It is not necessary that
if one is to understand the word “orange” something orange must exist.
And if we have a game in which the sample is orange, then it is nonsense to cite the
sample in substantiation of the claim that something orange must exist. This would be
like saying that there must be something a foot long because the Greenwich foot, the
paradigm, is a foot long. Or like saying that in order to speak about five things there
must be five things, where the latter, five letters, say, are the paradigm.
(AWL p.120)71
69
See TB 19/06/1915, p.66; TLP 5.634.
See TB 04/09/1914, p.3: “If logic can be completed without answering certain questions, then it must be
completed without answering them.”
71
The train of thought alluded to at the beginning of this passage is prominent in Russell's writings. Thus,
in the Lectures on Logical Atomism, Russell argues that one cannot understand the meaning of the word
“red” unless one has come across instances of red, nor convey its meaning except by pointing to such
instances, so that the symbol “red” is, strictly speaking, indefinable, hence, for the purposes of analysis, a
“simple” one (see Russell (1918) pp.194-195). For Russell, our ability to make sense of a symbol we have
never come across before is the mark of its not being simple (see Russell (1918) p.195). Wittgenstein
diagnoses a conflation between the concept of an example in the sense of an exemplar and the concept of an
example in the sense of an instance. Russell will have mistaken the need for a symbol for the need for an
object. In the context of showing how formally to reduce predicates to relations, Russell mentions the
possibility of equating “being red” with “being of the same color as this”, where “this” refers to a “standard
red thing” (see Russell (1918) p.206). But far from obviating the need to be acquainted with an instance of
70
20
The bearing of these considerations upon the issue of the relation between logic and its
application is brought to the fore here:
Russell and Ramsey thought that one could in some sense prepare logic for the
possible existence of certain entities, that one could construct a system for welcoming
the results of analysis. Beginning with 2- and 3-termed relations, of which one has
instances, one could claim to have prepared the calculus for 37-termed relations, of
which there are no instances. We tend to think that when we have found an example
of aRb we have found a phenomenon to which aRb is applicable. We have only found
a word in our language which behaves like aRb. Before an instance of aRb is found
there could be the word in the language. Constructing a relation does not depend on
finding a phenomenon. Discovering a word game is different from discovering a fact.
(AWL p.143)
The attempt to build up a logic to cover all eventualities (…) is an important
absurdity. We must remember that if we feel the need of an instance of an n-termed
relation we still have the symbolism for n things not standing in relation. The need is
for a sample, a paradigm, which is again part of the language, not part of the
application. Samples play the role played by the Greenwich foot, the existence of
which does not prove that anything is a foot long. The Greenwich foot itself is not a
foot long. To say 'Here is an instance of people being in love” is to take a sample into
our language. And to do this is to make a decision, not to discover anything.
(AWL p.143)
In his Theory of Knowledge of 1913, Russell takes the existence of a logical form to be a
non complex fact with which it is required that we be acquainted, prior to analysis, if we
are to understand any particular proposition of that form.72 Our being acquainted with
such a fact at once makes it possible for us to understand any such proposition and paves
the way for its analysis by ensuring that it be amenable to its strictures. Thus, were it not
for our being acquainted with the purely logical fact that “something has some relation to
something” (i.e. “∃(x,y,R).xRb”), we would not so much as make sense of the proposition
“Socrates loves Plato” (i.e. “aRb”). Wittgenstein agrees that if the mere existence of a
proposition does not testify to its being logically in order, then nothing could except the
existence of a logical fact, or rather our knowledge thereof.73 Conversely, if logic cannot
be held hostage to such knowledge, then a classification of logical forms according to their
types (a theory of categories) is at once out of place and superfluous,74 since “that
red, such a reduction traces all acquaintance with red things to the acquaintance with one single instance of
red. As we shall see, such a relational account of the meaning of “red” trades upon the very conflation
denounced by Kripke between defining in the sense of fixing the reference and defining in the sense of
giving a synonym. See Dolev (2007a).
72
See Russell (1913) p.114: “The form for all subject-predicate complexes will be the fact 'something has
some predicate'; the form of all dual complexes will be 'something has some relation to something'. The
logical nature of this fact is very peculiar. If we take some particular dual complex xRy, this has three
constituents x, R, and y. For similar reasons, 'something has the relation R to something' contains no
constituent at all. It is, therefore, suitable to serve as the 'form' of dual complexes. In a sense, it is simple,
since it cannot be analyzed. At first sight, it seems to have a structure, and therefore to be not simple; but it
is more correct to say that it is a structure.” Wittgenstein himself was for a time troubled by the appearance
that completely general propositions are simple. Witness the following entry from the Notebooks, which
echoes the passage from Russell just quoted: “We might also say that our difficulty starts from the
completely generalized proposition's not appearing to be complex. (…) It appears not to have a form but
itself to be a form complete in itself.” (TB 25/10/1914, p.18). But such appearance was soon to be dissolved
by the author of the Tractatus (see TB 31/10/14, p.31). By contrast, as late as in 1918, Russell still holds
onto the view that logical propositions at least present such an appearance (see Russell (1918) p.239).
73
See Wittgenstein TB 03/09/1914 - 04/09/1914, p.2-3.
74
See Wittgenstein TB 22/08/1914, p.2;
21
precedent (Präzedenzfall) to which we should always like to appeal must be involved in
the sign itself.”75
If Russell's conception were correct, first of all, there would be analytic propositions. For
there would be propositions that depict the world yet are necessarily true, in the guise of
members of such pairs of completely general propositions as the pair made of “(∃x,φ).φx”
and its negation “~(∃x,φ).φx”. In effect, a proposition depicting a purely logical fact would
be self-verifying, since the mere fact that it has the logical form that it has would make
such a proposition – whose sole means of depiction would lie in that form – true.76 Such a
proposition would be self-verifying in virtue of its being about itself. Second, its truth
would be presupposed by the sense of any particular proposition whose logical form it
depicts. Thus, the sense of a proposition would depend on the truth of another.
On the first score, Wittgenstein objects that the claim that logical propositions mention
logical forms is a self-defeating attempt at giving only half its due to the all-pervasive
character of logic.77 What is more, it assumes an asymmetry for which it is unable to
account. For it assumes that, of a completely general proposition and its negation, one and
only one is self-verifying (inasmuch as it has no thinkable negation), yet has no means to
discriminate between them.78
On the second score, Wittgenstein objects as follows:
I thought that the possibility of the truth of the proposition φa was tied up with the
fact (∃x,φ).φx. But it is impossible to see why φa should only be possible if there is
another proposition of the same form. φa surely does not need any precedent
(Präzedenzfall). (For suppose that there were only the two propositions “φa” and
“ψa” and that “φa” were false: why should this proposition only make sense if “ψa”
is true?)79
If at first Wittgenstein himself could not find a way around the unpalatable conclusion
that the sense of φa depends on the truth of (∃x,φ).φx, this was because he could not see at
first how else the existence of a location for φa within logical space could be guaranteed.
But if it were a logical fact that (∃x,φ).φx, then the holding of φa could no longer be
regarding as the holding of a state of affairs. It seemed as though, at the elementary level,
logical space was bound to shift under the circumstance that (say) the negation of no
elementary proposition is true.80
The way out of this nest of difficulties lies in the realization that the fact that (∃φ,x).φx is
not the logical form of “φa” after all, for the simple reason that it is not a logical fact in the
first place: it is a fact like any other.81 For φa to have the form that it has just is for the
form exhibited in (the proto-picture) φx already to show forth in φa. Thus it does not stand
in need of any precedent. How so? The answer is that the names comprising φa already
supply φa with its form, that there is no need for a form over and above the forms of its
75
Wittgenstein TB 01/11/1914, p.22.
See Wittgenstein TB 14/10/1914 - 15/10/1914, p.12.
77
Wittgenstein TB 18/10/1914, p.14: “A statement cannot be concerned with the logical structure of the
world, for in order for a statement to be possible at all, in order for a proposition to be capable of making
sense, the world must already have just the logical structure that it has.”
78
Wittgenstein TB 16/10/1914, p.13: “Now, however, it looks as if exactly the same grounds as those I
produced to show that “(Ex, φ).φx” could not be false would be an argument showing that “~ (Ex, φ).φx”
could not be false; and here a fundamental mistake makes its appearance. For it is quite impossible to see
why just the first proposition and not the second is supposed to be a tautology.”
79
Wittgenstein TB 21/10/1914, p.17. On the crucial importance of this strand of the Notebooks for an
understanding of the Tractarian argument for proto-elements, see Gandon (2002) p.82-83; Zalabardo (2012).
80
See Wittgenstein TB 15/10/1914, p.13.
81
See Wittgenstein TB 01/11/1914, p.22.
76
22
names.82 This is because a proposition is not a complex of names whose form is the
cement but rather the holding of a certain relation between names.83 And the holding of a
certain relation between names is neither a relation between names nor a complex of
names, but a certain fact.
Thus, on the one hand, so-called “logical propositions” are not genuine propositions (i.e.
propositions with sense) at all; they are not arrived at through a process of generalization,
as Russell thought. There is literally nothing for logical propositions to depict. There need
not and cannot be propositions asserting the existence of proto-pictures such as φx, and
(∃φ,x).φx is certainly not one.84 On the other hand, there are indeed completely general
propositions; only they are material propositions, standing on a par with all other
propositions,85 and possessing the same logical multiplicity as their instances.86 These two
points are the two sides of the same coin:87 the “kind” of generality that is the hallmark of
logic is not to be confused with the merely accidental generality of completely general
propositions.
At bottom, negation and quantifiers pose exactly the same problem and are to be handled
in the same way. Just as the sense of ~p (i.e. the possibility of being the case that ~p)
should not depend upon p being the case, so the sense of (i.e. the possibility of its being
the case that) φa, where “φx” reads “x is red”, should not depend upon there being some
object, say a', such that φa' is the case, nor should the sense of (i.e. the possibility of its
being the case that) aRb, where “xRy” reads “x loves y”, depend upon there being some
pair of objects, say (a', b'), such that a'Rb' is the case. Its making sense to say that “this is
not red” (while pointing to a thing) no more presupposes that there is at least one thing in
the universe that is red than it presupposes that this is red. The form of p shows forth in p
even if there is no situation of this form; the form of aRb shows forth in aRb even if there
is no situation of this form (i.e. of the form exhibited by the proto-picture xℛy, where x, y,
and ℛ are variables). To put the same point differently, the operations of negation and
quantification (whether existential or universal) do not operate upon unfinished
propositions, upon propositional “radicals” as it were. The operation of negation does not
take a proto-proposition as its basis. Operations of quantification do not take proto-types
(Urbilder, proto-pictures) as their bases. It is not the proto-type (Urbild, proto-picture)
exemplified by aRb (namely, the form exhibited by xℛy) which, on its own, functions as
a meter-stick against which the situation depicted by aRb is to be measured, but rather the
propositional picture aRb itself. Conversely a meter-stick used to measure a certain
situation is literally a proposition.
The passage from 1935 quoted before clearly rehearses the twofold objection to Russell
just recapitulated. There is a temptation to think that while the intelligibility of “a is red”
must be compatible with a not being red and the intelligibility of “a is not red” must be
compatible with there being no other sense for a to “be red”, and although they are
perhaps both compatible with there being nothing known to exist and to make an instance
of “x is red” true, yet they are not compatible with there being no logical form that be
known to exist no matter what and to be exemplified by “a is red”. The temptation is here
recast as the temptation to think that if “red” is to make sense, i.e. if it must be possible to
state of anything either that it is or that it is not red, there must be a standard of red that be
82
See Wittgenstein TB 01/11/1914, p.23-24. See Gandon (2002) p.88.
See Wittgenstein TB 04/11/1914, p.26; Wittgenstein TLP 3.1432.
84
See Wittgenstein TB 16/05/1915, p.48.
85
See Wittgenstein TB 22/10/1914 - 23/10/1914, p.17.
86
See Wittgenstein TB 31/10/1914, p.22.
87
See in this connection McGinn (2005) p.123.
83
23
known to exist and to be presupposed by ascriptions of red – where such a standard is
conceived as something like the instance of red par excellence, as it were The Red or the
Form of red.
Wittgenstein's response is that the need for a standard, if need there is, is precisely not the
need for an example in the sense of an instance but only the need for an example in the
sense of an exemplar. First, a genuine standard by means of which a name is defined is not
something that gives sense to that name when before it was empty. The standard meter is
not measured to be one meter long. The point is not so much that it is nonsense to say that
the standard meter (resp. the standard for red) is one meter long (resp. red) as that it is
nonsense to hold the statement of such a fact (assuming, for the sake of argument, that it is
one) to make true the existential generalization that there is something that is one meter
long (resp. red). Thus, the need for a paradigm of red, if need there is, is not the need for
an instance par excellence. Second, were an instance of red to ensure that “a is not red”
makes sense even if it is true, then a negative instance could do as well. Conversely, there
is no such thing as a negative standard. It would be nonsense to define “meter” by
stipulating that “meter” is not to refer to the length of this stick. One would not thereby (so
much as begin to) single out any length. There is no such thing as negative identification.
One may be “acquainted with” the standard meter only in the sense that one may be
familiar with the game of measuring.88
§11. The criticism of Russell’s claim that logical elements are only nameable that can be
ascribed to PI §50 is closely related to an objection mounted by Moore against Russell’s
unqualified contention that “existence is not a predicate”.89 The criticism turns on the idea
that the mere epistemic necessity of the existence of the designatum of a logically genuine
name does not entail its necessity simpliciter.
In “Is Existence a Predicate?” Moore concedes to Russell that “This exists” is
nonsensical if “exists” is used in the same manner as in “Some tame tigers exist” (i.e.
“There are tame tigers”).90 He insists that the contrast between “Some tame tigers growl”
and “Some tame tigers exist”, which shows up in the fact that the former asserts that some
values of “x is a tame tiger and growls” are true while the latter asserts only that some
values of “x is a tame tiger” is true, is not to be traced to “This is a tame tiger and exists”
being redundant but to its being nonsensical.91 Nevertheless, Moore argues, from the fact
that “This exists” is nonsensical as long as “exists” is used in the same manner as in
“Some tame tigers exist”, it by no means follows that “This exists” (where “this” is used
as in “This is a book”) cannot make sense when used in some other ways. Moore argues,
in effect, that “This exists” must make some sense or other, in particular, when it is used
by a person to say of a certain present sense-datum of hers that it exists, since otherwise
the truth of “This might not have existed” would become unintelligible. Moore’s point, in
other words, “is that ‘This might not have existed’ is analyzable as ‘It might be the case
that (it is not the case that (this exists))’, and this could have no meaning if its innermost
component did not.”92 As Moore puts it, that the statement “This exists”, so used, is
always true does not entail that it is necessarily true:
88
On this drastic reconception of Russellian acquaintance, see especially Floyd (forthcoming).
Moore (1936)
90
See Moore (1936) p.184.
91
See Moore (1936) p.185. Moore famously argues that, from the premise that “Some tame tigers exist”
means the same as “Some values of ‘x is a tame tiger’ are true”, it does not follow that “exist” means the
same as “x is a tame tiger” and “some tame tigers” the same as “x is a tame tiger”. Rather, what does follow
is that “This exists” (where “exists” is used in the same ways as in “Some tame tigers exist”) is nonsensical.
See also Prior (1967) p.145.
92
Prior (1967) p.145.
89
24
That “this exists” has any meaning in such cases, where, as Mr Russell would say, we
are using “this” as a “proper name” for something with which we are “acquainted”, is,
I know, disputed; my view that it has, involves, I am bound to admit, the curious
consequence that “this exists”, when used in this way, is always true, and “this does
not exist” always false; and I have little to say in its favour except that it seems to me
so plainly true that, in the case of every sense-datum I have, it is logically possible
that the sense-datum in question should not have existed – that there should simply
have been no such thing.93
Russell disposes of the notion of necessary truth on the ground that talk of a proposition
being necessarily true and talk of a proposition being always true are equally out of place.
Such notions apply to propositional functions, not to propositions. For a propositional
function to be necessary just is for it always to be true, i.e. for it to be true in all cases.94
Couched in Kripke’s terminology, Moore’s point is that, from the epistemic premise that
this could not turn out not to exist, the non-epistemic conclusion that it could not have
been the case that this should not have existed” cannot be derived.95 Even granting that
acquaintance with the designatum of a logically genuine name is necessary, it by no means
follow that the designatum with which one is thus acquainted cannot be held to exist
contingently.96
In Reference and Existence, Kripke considers and rejects Russell’s grounds for
maintaining the view that there must be logically genuine names, understood as names
whose designata are such that the issue of their existence or non-existence cannot be
raised. Such designata must be logically simple. Thus, only individuals can count as such
logically simple designata. The claim that existence is not a first-level predicate (i.e. that
individuals cannot be meaningfully ascribed or denied existence) ensues as a corollary.
According to Kripke, Russell’s grounds have to do with the analysis of negative
existential statements, whether in the indicative or in the subjunctive,97 and with that of
statements in which fictional names occur in subject position. As for Russell’s main
argument for the corollary claim, it runs as follows: “if existence applied to individuals, it
would be absolutely impossible for the property not to apply, and that this is characteristic
of a mistake”98.
Kripke traces the latter argument to two possible sources of confusion99, both of which
could account for the faulty inference that Moore denounced. A first source of confusion
resides in the ambiguity concealed in the sentence “it is absolutely impossible for it not to
apply”. It might be taken to mean either that ☐(x)∃(x) (i.e. that “it is necessary that
everything exists”) or that (x)☐∃(x) (i.e. that “everything has necessary existence”).100 A
second source of confusion might lie in a failure to keep sight of the distinction between
“what people would have been able to say in hypothetical circumstances, if they had
obtained” and “what we can say, of these circumstances, perhaps knowing that they don’t
obtain”.101 The latter confusion might tempt us into taking this line of reasoning:
93
See Moore (1936) p.188. See also Prior (1967) p.145.
See Russell (1918) chap. 5; (1919) chap. 15.
95
See Kripke RE p.36-37.
96
As Geach puts it: “Russell’s transition from ‘A genuine proper name must name something’ to ‘Only a
name that must name something is a proper name’ is of course just a howler in modal logic; here he paid for
his lifelong neglect of the subject. (There is just the same howler here as in passing from ‘What you know
must be so’ to ‘Only what must be so is really known’.” (Geach (1972) p.155)
97
Kripke RE p.19.
98
Kripke RE p.37.
99
Kripke RE pp.38-40.
100
Kripke RE pp.37-38.
101
Kripke RE p.39.
94
25
Suppose that (…) to express a proposition about Moses, and to use the name ‘Moses’
as a name, there has to be an object referred to, namely, Moses. Then how could
‘Moses does not exist’ ever have been true? For if there hadn’t been a Moses, we
wouldn’t have been able to use this name; we wouldn’t have been able to say so; and
perhaps even the proposition that Moses doesn’t exist itself wouldn’t have existed.102
To dispose of this apparent predicament, it is enough to appeal to the above distinction:
We do have the name ‘Moses’, and it is part of our language, whether it would have
been part of our language in other circumstances or not. And we can, of certain
hypothetical circumstances, that in those circumstances Moses wouldn’t have existed;
and that our statement “Moses exists” is false of those circumstances, even though we
might go on to say that under some such circumstances, had they obtained, one would
not have been able to say what we can say of those circumstances.103
It is important to realize that the second fallacy is not nearly as straightforwardly
noticeable as the first. That is to say, the fallacy is not always as obvious as in the
argument to the effect that, since New York might have been called “Vienna”, Vienna
might have been in the United States. In this respect, the temptation to “identify what
people would have said in certain circumstances, had those circumstances obtained, with
what we would say of certain circumstances, knowing or believing that these
circumstances don’t obtain”104 stands on a par with the temptation to assimilate questions
about counterfactual situations to epistemic questions. From the correct premise that
Sherlock Holmes could turn out to exist, we are apt to draw the incorrect conclusion that it
could have been the case that Sherlock Holmes should have existed.105
As Kripke observes in the first Lecture of Reference and Existence, Moore’s point
suffices to establish that Tractarian elements cannot be individuals in Russell’s sense. For
what holds of the designata of Russellian names, that they exist indubitably yet not
necessarily, precisely does not hold of the designata of Tractarian names, notwithstanding
the fact that empty names are excluded from the ranges of Russellian and Tractarian
names alike. Kripke writes:
It is interesting to note that the two requirements that they place on the existence of
those objects – one, indubitability, and the other, the Wittgensteinian requirement that
they have necessary existence – are incompatible. For it would seem, at least to me,
that nothing more plainly has contingent existence than one’s own immediate sensedata, one’s own immediate visual impressions.106
It has been a bit of a question, in the exegesis of the Tractatus, whether
Wittgenstein’s objects are in fact Russellian objects, whether they are in fact one’s
own immediate perceptions, or at least include them. I don’t want to go into an
exegetical question, and perhaps couldn’t conclusively argue this, but it would seem
that if Wittgenstein had his wits about him on this matter, the objects couldn’t be
one’s own immediate sense-data, because such objects would fail to satisfy the most
elementary requirements of the theory. Therefore, unless he simply failed to notice
this, he didn’t believe that these were the objects.107
102
Kripke RE p.38.
Kripke RE p.39.
104
Kripke RE p.40.
105
Kripke RE pp.41-42. Kripke takes himself to have succumbed to the latter temptation in subscribing, in
some earlier piece of work (Kripke (1963)), to the standard default view that it could have been the case that
Sherlock Holmes should have existed, just as it could have been the case that Napoleon should not have
existed. See Kripke RE pp.40-42.
106
Kripke RE p.17.
107
Kripke RE p.18.
103
26
Of course, that the objects of Russell and those of Wittgenstein are meant to meet distinct
and even incompatible requirements does not by itself preclude the possibility that the
argument for the latter should be vulnerable to a parallel (if distinct) charge. Indeed,
construed in a certain way, the Tractatus’ argument for the existence of proto-elements
lies open to the charge of resting upon a misunderstanding of the workings of modal
evaluation, just as Russell’s does. In Philosophical Remarks, Wittgenstein retrospectively
sums up the Tractarian conception of proto-elements as follows:
What I once called “objects”, simples, were simply what I could refer to without
running the risk of their possible non-existence; i.e. that for which there is neither
existence nor non-existence, and that means: what we can speak about no matter what
may be the case.108
Admittedly, this passage might seem to invite a reading of the Tractatus’ argument for
the existence of proto-elements along the following lines: if there were no substance,
everything would exist contingently; but then whether a proposition had sense would
depend on whether another is true; and so we could not so much as make pictures of the
world, i.e. make any sense; therefore, of necessity, there is substance.109
The Tractatus’ argument, if it is construed along these lines, can be shown to comprise
the following five tenets.110 First, Wittgenstein’s argument is first and foremost an
argument for the necessary existence of proto-elements and only derivatively one for their
simplicity.111 Second, it coheres with the assimilation of the reference of a name to its
bearer (which assimilation is denounced in PI §40 and its vicinity). Third, the Tractarian
notion of name is regarded as a reformation of the ordinary notion (from which it follows
that it makes sense to ask what kind of familiar entities Tractarian objects are). Fourth, the
argument for the possibility of names collapses into an argument for the indispensability
of singular terms. Fifth, and finally, the argument for the possibility of names collapses
into an argument for the existence of such names. Certainly, the Tractatus’ argument for
proto-elements, so read, is part and parcel of the target of PI §55112 – a fact which may in
turn seem either to support this reading113 or (if one does not go along with this reading) to
disqualify the assumption that the Tractatus’ argument lies within the purview of PI
§55114.
So construed, the Tractatus’ argument for proto-elements evidently lies open to the
charge of resting on equivocation.115 So read, the Tractatus conflates two distinct notions
108
Wittgenstein PB §36 p.72.
See Proops (2004) p.114, p.120; Proops (2007) section 3.
110
All five tenets are criticized by Ishiguro in her landmark essay. See Ishiguro (1969) (i) p.; (ii) p.26, p.40;
(iii) p.37; (iv) p.42-45; (v) p.43, p.46.
111
See e.g. Proops (2004) p.110.
112
Wittgenstein (1953) §55:
“What the names in language signify must be indestructible; for it must be possible to describe the state of
affairs in which everything destructible is destroyed. And this description will contain words; and what
corresponds to these cannot then be destroyed, for otherwise the words would have no meaning.” I must not
saw off the branch on which I am sitting. One might, of course, object at once that this description would
have to except itself from the destruction.—But what corresponds to the separate words of the description
and so cannot be destroyed if it is true, is what gives the words their meaning—is that without which they
would have no meaning.—In a sense, however, this man is surely what corresponds to his name. But he is
destructible, and his name does not lose its meaning when the bearer is destroyed.—An example of
something corresponding to the name, and without which it would have no meaning, is a paradigm that is
used in connexion with the name in the language-game.
113
See Ahmed (2010) p.28.
114
See Zalabardo (2012) p.147-149.
115
See Proops (2004) p.121, (2007) section 3.2. See also Ahmed (2010) p.28. In the end, Ahmed rejects
this reading.
109
27
of “possible circumstance” due to its misunderstanding or (to use one commentator’s
rather euphemistic formulation) due its “rudimentary understanding of the workings of
modal evaluation that Wittgenstein had at his disposal”.116 The suggestion is that the
Tractatus’ argument for the necessary existence of proto-elements, like Russell’s
argument for the view that “This exists” cannot be regarded as contingently true, conflates
the truth or falsity of a propositional sign as uttered in a possible situation and its truth or
falsity as assessed with respect to a possible situation.
In light of the above, the Tractatus’ argument can easily be exposed. For the
counterfactual statement “N might not have existed” to make sense, that is to say, for the
statement “N does not exist” to be assessable as true or false in non-actual worlds, and
hence for the name “N” to contribute a referent to this statement, N need not exist in any
of those non-actual worlds; it need only exist in the actual world, that is to say, in the
world in which the counterfactual statement “N might not have existed” is being uttered.
In other words, N need only exist in the “context of utterance” that contributes to the
statement “N might not have existed” being evaluable, as distinct from those
“circumstances of evaluation” in the light of which this statement is evaluated.117
It is noteworthy that, although this objection and the reading that falls prey to it both
descend from Kripke’s thought, Kripke himself refrains from putting forward either of
them in the course of his sustained critique, in Reference and Existence, of the common
core of Russell’s and Wittgenstein’s respective arguments in favor of the view that the
designatum of a logically genuine name must be an object such that the question of its
existence and non-existence cannot so much as arise. Kripke’s caution is in order: the
second fallacy cannot be imputed to the Tractatus. The Tractatus can have no room for
the notion of circumstances in which a proposition – i.e. “a propositional sign in its
projective relation to the world” (TLP 3.12) – would lack the sense that it actually has.118
Nor can it be held to lean towards this view.119
Kripke’s qualms about Wittgenstein’s argument for simple names in the Tractatus differ
significantly from his qualms about Russell’s. Kripke takes Russell to have mistaken the
non-epistemic necessity that goes with rigidity for an epistemic necessity of sort. He takes
Wittgenstein to have inflated non-epistemic necessity into necessary existence.
§12. The above, “ontological” reading of the Tractatus’ argument for the existence of
proto-elements is informed by a view of analysis that is Russellian in its essentials. Such a
view stands at odds with Wittgenstein’s. Russellian analysis is “bottom-up” insofar as
“Russellian acquaintance provides a self-standing conception of the terminus ad quem of
analysis to guide the activity of analysis”, whereas Wittgensteinian analysis is “ resolutely
top-bottom”120.
If we are to understand the Tractarian view of analysis, we must begin at the beginning,
namely at 3.23:
The requirement of the possibility of simple signs is the requirement of the
determinacy of sense.
In effect, the so-called “argument for substance” (TLP 2.0211-2.0212) must be read in the
light of 3.23. The deflationary implication of section 3.23 is that the requirement that
simple signs be possible is nothing over and above the requirement that sense be
116
Proops (2004) p.122.
See Kaplan (1989a), (1989b).
118
See Zalabardo (2012) p.124.
119
Pace Proops (2004).
120
Ricketts (forthcoming)
117
28
determinate. Now, the requirement that sense be determinate is constitutive of sense as
such. That is to say, its very nature imposes such a requirement upon sense. It is not one
that sense might conceivably fail to meet. But the determinacy of what we mean by our
ordinary, unanalyzed propositions cannot fall short of the full determinacy of their sense,
such as their full analysis would put on display. Their prima facie sense (as we might call
it) is their sense. The conjunction of these two claims entails that the determinacy that is
required of sense cannot be contingent upon our meeting epistemic requirements that we
might conceivably fail to meet.
Thus the logical articulatedness characterizing our ordinary propositions as they stand
must be such that we are not exposed to finding out subsequently, through further
analysis, what it was exactly that we had meant – or, to put things the other way around,
that what we had meant was not exactly what we had presumed). Complete analysis, if,
per impossible, we could achieve it, would merely put on display how it is exactly that we
did mean exactly what we did. If the sense of our ordinary, unanalyzed propositions is not
to be vulnerable to being exposed as indeterminate by further analysis, then we must be
deferring to its findings from the start. What we may not or cannot know, we need not
know either. For us to take care of the determinacy of our meaning just is for us to let it
take care of itself. Thus, the only epistemic requirement laid upon our ability to mean what
we say is that we should defer to the non-epistemic dimension of meaning. The Tractarian
vision of language is, in that sense, a resolutely “instrumentalist” one: our ‘acquaintance’
with ordinary language, in the sense of our familiarity with the ordinary language that we
master, dispenses us from the necessity of any ‘acquaintance’, in Russell’s sense, with
objects and their forms.
What this means is that the measure in which we trust our meaning to take care of itself
must already show forth – must as it were already be palpable – in our ordinary
propositions as they stand. To understand this, in turn, it is necessary and sufficient to
realize that the indeterminacy evinced by ordinary propositions, far from being a threat to
the determinacy of their sense, is their very way of securing the latter. This comes out
clearly from section 3.24, which ties together the argument for proto-elements
(Urelemente) and the argument for proto-types (Urbilder):
When a propositional element signifies a complex, this can be seen from an
indeterminacy in the propositions in which it occurs. In such cases we know that the
proposition leaves something undetermined. (In fact the notation for generality
contains a prototype.)
With this in mind, we may attain a better understanding of the character of the
inconsonance between Russell and Wittgenstein’s respective arguments for the possibility
of simple names. As Ryle points out in “Ontological and Logical Talk in Wittgenstein’s
Tractatus”121, Wittgenstein’s view that “the understanding of general propositions
depends palpably on that of elementary propositions” (TLP 4.411) directly gainsays
Russell’s view that the existence of elements is presupposed by logic, in the sense that the
existence of simples can and must be deduced “from the fact that ordinary expressions
must be dissectable up to the point where we would reach indissectable bones, if only we
could be thorough”, even though “we have no logically proper names for the subjects of
our ultimate propositions, and we are acquainted with no such subjects”122. As Ryle
emphasizes, “the obvious objection to this is that it follows that we never knowingly talk
sense”, since “you can’t talk sense by constructing general and compound propositions out
121
122
I am grateful to Kelly Jolley for drawing my attention to Ryle’s piece.
Ryle (1999) p.102.
29
of ingredients which are mysteries.”123
The theory of acquaintance subtending Russell’s account of simples jars with his analysis
of definite descriptions. On Wittgenstein’s view, the latter has the merit of dispelling the
appearance that our capacity to mean what we say is hostage to matters of fact.124 For it
shows that the capacity of sentences to say something true or false “is not dependent on
whether any definite description they may contain is satisfied”125. This is the one respect
in which the Tractatus can be said to regard the Russell’s view of analysis as superior to
Frege’s and to take its cue from it.126
Russell’s original sort of analysis goes some way to letting us see what sign a
sentence is, of the general sort to which sentences as such belong, by showing it
maintains truth-valuedness throughout variations in truth value of a particular range
of sentences, whose falsity we might have thought deprived it of any truth value.127
What Russell’s analysis of definite descriptions goes some steps toward showing is that
“the capacity to say something determinately true or false” is internal to the particular sign
that a sentence is just to the extent that this particular sign is “capable of comparison with
reality, yielding true or false, regardless of the truth or falsity of any sentence”128. The
chief virtue of Russell’s analysis, on this reading, is not so much that it resolves the puzzle
of singular negative existentials, as that it resolves at once and uniformly both this puzzle
and the puzzle arising from the meaningfulness of statements featuring empty names.
Russell’s treatment of existence as a second-order property is, in Kripke’s terms, “more
unified” than Frege’s.129
As Kripke points out, in Russell’s thought, the introduction of logically proper names,
inasmuch as it is specifically tailored for the requirements of his theory of knowledge by
acquaintance (i.e. inasmuch as their bearers are defined as being such that one cannot
doubt their existence), and the elimination of garden-variety proper names secured by their
analysis as definite descriptions in disguise, concur to dispose of one and the same
difficulty: namely, the paradox raised by negative singular existentials. In their
conjunction, in effect, the two moves have the result of blocking the paradox from ever
arising in the first place. For either the apparently paradoxical negative singular existential
statement is analyzed away into a general statement that no longer looks to ascribe nonexistence to its subject, or no sense could be made of an existential statement (whether
negative or positive), as the issue of existence simply does not arise in the nature of the
case. That the two moves should thus conspire to a single achievement is hardly trivial,
given that the former infringes the very principle that the latter vindicates: the context
principle. What links them up, in the framework of Russell’s philosophy, is Russell’s view
123
Ryle (1999) p.102.
See also Quine (1951) §27: “It is awkward, in general, to let questions of meaningfulness or
meaninglessness rest upon casual matters of fact which are not open to any systematic and conclusive
method of decision.” Note that for Quine “The artificial dodge of dispensing with primitive names in favor
of descriptions or other abstracts is a way of maintaining control of vocabulary independently of questions
of fact.”
125
Diamond (1991) p.189.
126
See Diamond (1991) Section II.
127
Diamond (1991) p.190.
128
Diamond (1991) p.191.
129
Kripke (2013) p.11. See also Quine (1948). Although in that essay Russell’s analysis of definite
descriptions gets introduced as a way out of the “old Platonic riddle of nonbeing” arising in connection with
negative singular existentials, Quine makes it clear that Russell’s analysis bears on this riddle insofar as it
refutes the assumption on which it turns: “Russell, in his theory of so-called singular descriptions, showed
clearly how we might meaningfully use seeming names without supposing that there be the entities allegedly
named.” (Quine (1948) p.5)
124
30
that knowledge by description at once outstrips knowledge by acquaintance (since it
provides indirect knowledge of things (i.e. knowledge of things with which we are not
acquainted), in particular knowledge of their existence) and rests upon it (since, according
to the so-called “principle of acquaintance”, “Every proposition which we can understand
must be composed wholly of constituents with which we are acquainted.”).130
Not only does the Tractatus disentangle what Wittgenstein regards as the true merit of
the theory of definite descriptions (namely, that of securing the determinacy of sense)
from Russell’s principle of acquaintance (after the manner of, say, Quine)131, but, more
radically, it also disentangles its merit from the function that it shares in Russell’s
framework with the introduction of logically proper names: namely, that of blocking the
paradox of negative singular existentials. Reversing the onus of match between the two
theories as conceived by Russell, Wittgenstein identifies the rationale for the introduction
of simple symbols (whose category he equates with that of simple names)132 with what he
regards as the true rationale for the elimination of definite descriptions.
§13. The gap between Tractarian names and Russellian names is even wider than so far
suggested. To bring out the gulf separating them, it suffices to note that, from the claim
that maximally general propositions are still genuine material propositions, it ensues that
the requirement that simple signs be possible is not identical to the requirement that
irreducibly singular terms be indispensable.133
The Tractatus resists the line of thought, prominent in Russell, that supports the
identification between these two requirements. The Tractarian argument for substance (i.e.
proto-elements) rests neither upon the identification of the references (Bedeutungen) of
names with the objects for which they deputize (vertreten), nor on the idea that, unless it
were tied up to the world by means of signs that cannot fail to refer without losing all
significance, our language would lose its grip on the world. To see this, we need only
advert to Wittgenstein's claim that names can be completely dispensed with in our
description of the world, as the world could be completely described by means of
completely general propositions (5.526):
We can describe the world completely by means of fully generalized propositions, i.e.
without first correlating any name with a particular object. / Then, in order to arrive at
the customary mode of expression, we simply need to add, after an expression “There
is one and only one x such that … ”, the words: “and this x is a”.134
The Tractatus holds that there are irreducibly singular terms (i.e. names), but not that
such terms are indispensable. What is required is only that names be possible. The world
may be completely described, indifferently, either by means of the collection of all the
130
See Russell (1912) Chapter 5.
See Quine (1948). For Quine the fundamental lesson of Russell’s analysis of definite descriptions –that
variables of quantification, not names, carry the weight of reference (see Quine (1948) p.6, p.12) – runs
counter to Russell’s own account of the role of names. Russell holds, in effect, that “you cannot name
anything you are not acquainted with” (Russell (1918) p.201) and that you cannot be acquainted with
anything unless it is a simple.
132
In The Philosophy of Logical Atomism, by contrast, Russell regards the category of “simple symbols” as
wider than that of genuine “names”, and correlatively the category of “simples” (a “simple” being what
cannot be symbolized except by means of a simple symbol (see Russell (1918) p.194)) as wider than that of
“particulars”. Acquaintance is necessary both for understanding simple symbols in general and for
understanding names in particular. But to understand a simple symbol that is not a name (such as, say, the
predicate “red” (see Russell (1918) pp.194-195), mere acquaintance with what it designates (being red) is
not enough: “you have to know what is the meaning of saying that anything is red.” (Russell (1918) p.205)
133
See Ishiguro (1969) p.42-46; Ricketts (2014) section 3.
134
Wittgenstein TLP 5.526. See also Wittgenstein TB 16/10/1914.
131
31
true elementary propositions (4.26), or exclusively by means of true completely general
propositions (5.526a), as the latter settle the truth-values of the elementary propositions
containing the names introduced on their basis (5.526b).135 Names do not anchor language
into the world by pinning it to objects.136
It follows from 5.526 that the argument for proto-elements cannot be that while a general
proposition like “(∃x)φx” has sense even if its false (i.e. if there is no object), a singular
proposition like “φa” cannot so much as make sense unless a could not fail to exist. What
can be said is only that “φa” could not so much as make sense unless the name “a”
existed, be part of the language – if only as a dummy name introduced through the
stipulation that it is to refer to whatever the actual true instance of “φx” talks about,137 like
the free variable introduced in a deduction by applying the rule for existential instantiation
in a natural deduction system138. Thus, in the Tractatus, not only is Wittgenstein not
moved by the pattern of reasoning, familiar from the work of Strawson and his epigones,
according to which the existence (not merely the possibility) of singular thoughts is a
precondition of thinking as such, but he contests it.139
If Tractarian names are dummy names, then they display referential rigidity. For it is in
the nature of a free variable under an assignment that it should refer no matter what. It is
in fact the very paradigm of a rigid designator.140 Thus, if Tractarian names are dummy
names, then Wittgenstein's decision to exclude ordinary names like “Nothung” from
counting as names in the logical sense, on the ground that the statement “Nothung has a
sharp blade” retains its sense even if the bearer “Nothung” no longer exists (because, say,
the sword is broken), should not be blamed on a conflation of the notions of bearer and
reference. For it may “show not that Wittgenstein wrongly identified the notions of bearer
and reference in the Tractatus but rather that although he was not articulate about this, he
had already realized that talk about reference of names is not like talk about the bearers of
ordinary names.”141 In other words, inspired by the behavior of ordinary proper names,
whose reference outlives the bearer, he had discerned that what characterizes a name, in
contrast to a description, is not that its referent cannot fail to exist, but that it refers to it no
matter what. In effect “just as names are permanent in our language, so according to
Wittgenstein objects are unalterable and persistent (bestehend) (2.0271)”.142
§14. In the light of this understanding of Tractarian names, we can revert to the
Tractarian notion of a proto-type or proto-picture (Urbild). Prototypes (Urbilder) are what
will have become of the logical forms that Russell sought to draw up the inventory of,
insofar as they were supposed to be indefinable objects of an acquaintance of some kind (a
“logical experience”). The forms of elementary propositions and those of the names
comprising them are what will have become of Russellian logical forms insofar as they
were supposed to be necessary. For a sign in an ordinary proposition to function as (if it
135
See Ricketts (2014) section 3.
See Sullivan (1996) p.205.
137
The introduction of the dummy name “a” is parasitic upon the introduction of the dummy singular
proposition ‘fa’. See Wittgenstein TB 09/07/1916 p.75: “Do not forget that ‘(∃x)fx’ does not mean: there is
an x such that fx, but: there is a true proposition ‘fx’.”
138
See Ishiguro (1969) p.45-46; Ricketts (2014) section 3.
139
The point holds a fortiori, I take it, for the Philosophical Investigations.
140
See Kaplan (1989a) p.484; (1989b) p.571-573. Ishiguro would seem to err in maintaining that “in this
example since we introduce the name ‘a’ by saying ‘(∃x)fx and this x is a’, it would be quite impossible to
envisage the a as not having the property f.” (Ishiguro (1969) p.45) Given the stipulation, the truth of fa is a
priori. This does not entail that it is necessary.
141
Ishiguro (1969) p.40.
142
Ishiguro (1969) p.41.
136
32
were) a simple sign just is for it not to function as a complex one; and for it not to function
as a complex one just is for the composition (i.e. inner structure) of what it is apparently a
name of to be immaterial to the truth-conditions of the proposition.
At the surface level, “simplicity and complexity are internal features of elements of
representation, not external, metaphysical characterizations of what they represent”,143 so
that for signs to be handled “ ‘as if’ they were simple is for them to be simple.”144 By
contrast, for a sign to be a sign concatenated in an elementary proposition, that is to say,
for it to be a simple sign (i.e. a name), is not just for it not to refer to something complex
or to refer to a non-defined thing, but for it to refer to a simple (i.e. an indefinable thing, a
proto-element) as combined in a state of things with other simples (i.e. indefinable things,
proto-elements). This is the deep level at which the paradigm constituted by Russell's
analysis of definite descriptions operates. At this level, its presupposing some
contingencies signals that a sign is not genuinely simple, i.e. not a genuine name.
The Tractarian concept of a name is not meant to supplant our ordinary concept of a
name on account of the latter's failure to measure up to the exacting standards of logic; nor
is the idea of a completely articulated language meant to capture the ordinary functioning
of language.145 Ordinary proper names remain our best model for conceiving the genuine
names among which we know they cannot figure.146 The two levels simply coexist. The
theory of prototypes bridges the gap between the two by making the acknowledgment of
this gap internal to the first. Prototypes obviate the epistemic need for complete analysis,
thereby testifying to the possibility of the latter.
While the signs that function as (if they were) simple signs in our ordinary propositions
function as the fixed points of our meaning, as so far articulated, so that the possibilities
whose non obtaining their use presupposes are consigned to the background and the
assessability of those ordinary propositions is left unrestricted, their forms are nevertheless
contingent upon the non obtaining of these possibilities. Conversely, while necessary,
objects and their various forms are not knowable a priori, that is to say prior to the
application of logic in analysis.147 What is more, they cannot be known individually.148
Thus, far from obliterating the distinction between epistemic necessity and non epistemic
necessity, the Tractarian view of analysis turns on a structurally similar distinction, that
between surface-level semantic necessity and deep-level semantic necessity. The Tractatus
does not collapse them. If anything, it is torn between them. As we shall see in the last part
of this chapter, PI §50 encapsulates a diagnosis of just that form.
In ascribing to the early Wittgenstein the claim that objects are necessary existents,
Kripke fails to realize that such a claim stands at odds with Wittgenstein’s understanding
of the requirement of the determinacy of sense. This is not to say, however, that Kripke
himself conflates the rigidity that the determinacy of sense requires with a necessary
existence of some kind. On the contrary, his conceptual apparatus allows us to see how the
rigidity of the dimensions of logical space can be a matter of the actuality of the actual
world, rather than a matter of the necessary existence of “elements” whose combinations
are supposed to “actualize” antecedently given possibilities.
143
Sullivan (2003) p.85.
Sullivan (2003) p.85.
145
See Ishiguro (1969) p.37; Sullivan (2003) p.80; Ricketts (2014) section 3.
146
See Ishiguro (1969) p.37; Sullivan (2003) p.86.
147
This paragraph draws on Sullivan (2003) p.83.
148
See Ricketts (2014) section 3.
144
33
IV.
Towards an Alternative Reading of PI §50
§15. We are now in a position to return to PI §50 at last. The zigzag paths taken by
Philosophical Investigations reflect its conviction that there is no such thing as being
finished with a philosophical topic – let alone a philosophical problem.149 Although it is
regularly silenced by the “voice of correctness”, the “voice of temptation” can never be
stifled. What grammatical investigations achieve is inherently disappointing, because
neither able nor meant to relieve us definitively from metaphysical restlessness.150
However, that a section or run of sections is, due to the very nature of these investigations,
but a sketch (or a snapshot) of a wide field of thought travelled over crisscross in every
direction (PI Preface) does not mean that it may not have a definite point, nor even that it
may not take a single definite path. Nor does it mean that it may not be “sketched knowing
that it must be, and gets in time, transformed in order to take its place”151 in the run of
sections to which it belongs. Section §50 is a case in point.152
The ultimate deflationary point of §50, I submit, is not that saying that we could not so
much as think that something is red if red were not a unit of sense amounts to saying that
our language-game must counts a paradigm for red among it means of representation. That
is, the true point of §50 is not that what is required is that red should be a means of
representation in our language-game, not that there should be something red among the
things to be represented. On the contrary, the true point of §50 is that saying that we could
not so much as think that something is red if red were not a unit of sense merely amounts
to saying that our language-game does contain a paradigm of red – not to saying that our
language-game must counts such a paradigm among its means of representation. The
closing insight of §50 is that the requirement that there be units of sense is not so much
149
Anscombe (2011) p.189.
Cavell (2005) p.195, p.209.
151
Cavell (1979) p.5.
152
The internal structure of §50 mimics that of an improvised but guided exchange (like one between
pupils under the lead of their teacher). Hence our sense that it is crafted, conspicuously not improvised. You
might say that “what must be sketched must be written.” (Cavell (1979) p.5) The exchange in question is not
happily construed as a head-on clash between the two voices of “temptation” and “correctness”. The writing
of §50 can be said to bespeak a third pressure, namely, that of “the attainment of silence, say
unassertiveness” (Cavell (1995) p.178), both insofar as §50 is punctuated by neutral interventions (those of
the teacher, as he tries to help the conversation move forward, while consciously abstaining from making
assertions of his own) and insofar as all its opinionated interventions prove to be question-begging, or
biased, except for the one that brings it to a close (i.e. the one which secures silence, if only momentarily).
Attempts at dislodging a metaphysical temptation that do not scratch below its surface can only succeed in
fuelling it. The first response elicited by the opening question of §50 encapsulates just such an attempt. It
lacks critical acumen. It is worthy of a disciple – i.e. an uncritical adept – of the (non existent) doctrine of
Wittgensteinianism. Its insufficiency prompts the reinstatement, by a second voice (think of it as that of a
second pupil), of the very metaphysical urge that it was meant to dislodge (“being cannot be attributed to an
element, because…”). To move past this standoff, the teacher offers to consider an object of comparison
(“But let us consider an analogous case!”) (= C1). Whereupon the disciple seizes upon what the teacher has
just said as if, properly construed, it decisively pleaded for the doctrine which he favors (“But this is, of
course, not (…)”) (= C2). (The standard reading of PI §50, which unqualifiedly ascribes C2 to Wittgenstein,
can hardly account for the dash before C2.) Which in turn moves the teacher to introduce a second object of
comparison (“Let us imagine samples of color…”) that, while contrived, is not as question-begging as the
first. Its relevant features are brought out. (“This sample is an instrument of the language, (…)”). The first
pupil is able to draw the implications for the elements of language-game (48) (“And just this holds for
(…)”). His way of cashing them out, however, betrays a failure to get to the bottom of the comparison, a
failure fully to grasp its point. Or so it appears in the light of the caveat (“still, (…)”) on which the teacher's
reformulation (“What, on the face of it, there has to be…”) ends. Although commentators have paid scant
attention to it, the caveat is what brings the section to a close, what enables its voices to attain silence. It
encapsulates that section's point.
150
34
one that is laid down upon our language as one that is laid down by it – that is, by us.
Which is to say that it is really no genuine requirement at all. Or so shall I argue, drawing
on Kripke's work, in the last paragraph of this section. As we shall see, this point does
constitute a genuine criticism of the Tractatus – one that no longer turns on mistaking one
of the Tractatus' targets for one of its views.
Thus, PI §50 can be read as a new formulation of a crucial criticism made by the
Tractatus only up to a point. That it can be so read is nonetheless all the more important as
the criticism in question is standardly mistaken for a criticism of the Tractatus by the
Investigations. That PI §50 can be read both as elaborating upon the Tractatus' criticism of
the specifically Russellian view of simplicity and as mounting a criticism against the
generic view of simplicity vindicated by the Tractatus, is due to the ambiguity concealed
in the counterfactual argument rehearsed at the beginning of §50b. This counterfactual
argument admits of both a Russellian reading and a Tractarian reading, the latter of which
is premised on the rejection of the former. It should be clear by now that read in the
former way, it lies open to the charge of conflating epistemic possibility and nonepistemic possibility. Russell will have wrongly inferred from the epistemic necessity of
prototypes to their non-epistemic necessity (i.e. to their necessary existence) (this is the
non-sequitur denounced by Moore and Kripke), thereby mistaking prototypes for
elements. Conversely, he will have wrongly inferred from the non-epistemic necessity of
elements to their epistemic necessity (i.e. to the requirement that we be acquainted with
them), thereby mistaking elements for prototypes. Read in the latter way, the argument
trades on no such equivocation. The Tractatus drives a wedge between the surface-level
semantic necessity of prototypes and the deep-level semantic necessity of elements.
Depending on how the counterfactual argument of §50b is read, it incurs different charges.
As against the argument construed in the former (i.e. Russellian) way, the charge mounted
by §50c is that of a failure, on the part of Russell, to realize that the requirement that there
be prototypes (surface-level forms) reduces to the surface-level semantic requirement that
there be standards (in the ordinary sense in which the standard-meter or the standard-sepia
are standards) and is not to be conflated with the deep-level semantic requirement that
there be elementary conditions of sense. As against the argument construed in the latter
(i.e. Tractarian) way, the charge mounted by §50c, we shall see, is that of a failure, on the
part of the author of the Tractatus, to realize that the requirement that there be units of
sense, if sense is to be determinate, reduces to the surface-level semantic requirement that
there be prototypes or standards (in the ordinary sense) and is not to be inflated into the
deep-level semantic requirement that there be elements existing in their own right – be
they construed as the intangible dimensions of sense. For sense to be determinate is indeed
for there to be units of sense; but for there to be units of sense just is for certain words to
be in circulation, for them to be common currency among us.
§16. The pair of points on which Kripke fastens (C1 and C2) are quite evidently meant to
contribute to disarming the opening argument of §50b.153 However, to regard such
contribution as straightforward and self-contained, as the standard reading and the antistandard reading equally do, is to assume that the “analogous case” introduced by C1 is too
familiar to give rise to puzzles of its own.154 But that seems almost exactly wrong. It is
worth dwelling for a moment on the wording of C1. C1 clearly stands on a level with the
claim criticized in the passages from the 1935 lecture foreshadowing PI §50, namely:
C0
153
154
There necessarily is one thing that is one meter long, and that is the standard
See above section 1.2.
See above section 1.3.
35
meter in Paris.
The overall logical form of C1 (“There is one thing that (…), and that is the standard
meter in Paris”) is reminiscent of that of C0. At the same time, with respect to its content,
C1 is reminiscent of the point made against C0 (to the effect that “The Greenwich foot is
not a foot long” (AWL p.120)). Insofar as C1 implies the falsity of C0, C1 might thus seem
unambiguously to correct the temptation that expresses itself in both C0 and the contention
that “being cannot be ascribed to an element”.
But that C1 has, except for its modalization, the same logical form as C0, namely that of
an existential generalization followed by mention of its basis, should make us suspicious
of its innocuity. Certainly, C1 is so worded as to allow for being read as C1' or C1'':
C 1'
There necessarily is one thing whose essence is to be one meter long, hence
such that it can be stated of it neither that it is nor that it is not one meter
long, and that is the standard meter in Paris.
C1''
There necessarily is one thing whose essence is to be one meter long, hence
such that it can be stated of it neither that it is nor that it is not one meter
long, and that is the unit of length called “the meter”.
So read, C1 ensues from an argument analogous to the one under criticism in §50.
Depending on whether it is read as C1' or C1'', C1 ensues from argument A1 or argument A2
below:
A 1'
If there were not one thing whose essence is to be one meter, that is to say,
such that it can be stated of it neither that it is nor that it is not one meter long, to wit,
the standard meter in Paris, then nothing could be stated either to be or not to be one
meter long.
A1''
If there were not one thing whose essence is to be one meter long, that is to
say, such that it can be stated of it neither that it is nor that it is not one meter long, to
wit, the unit of length called “the meter”, then nothing could be stated either to be or
not to be one meter long.
Both arguments are analogous to the one adduced at the beginning of §50b in support of
the contention that “being cannot be ascribed to an element”, namely:
If there were not a thing whose essence is to be (i.e. exist) for “A” to designate, then
there would be nothing that A could be stated to be or not to be, so that there would
be indefinitely many things that could not be said to be (i.e. exist) or not to be (i.e.
exist).
The pointed parallel between the joint denial contained in C1 and the joint denial about
elements adds to the overall congruence in form between C1 and C0 to cast doubt on the
metaphysical innocuity of C1, even as qualified by C2).155 C1 cries out for contextual
qualifications that C2 fails to adduce.
Note that if C1 is read as C1'', then the “analogous case” is no longer the standard meter in
Paris but the unit of length called “the meter”. Certainly, in the passages from the 1935
lecture foreshadowing §50, the second term of the analogy involving a canonical metrical
standard is not that canonical standard itself but rather the metrical unit or the name of that
metrical unit: the “analogous” case, that is, is not the canonical standard but the meaning
of the name of the metrical unit defined through it. Furthermore, the center of gravity of
the passages from the 1935 lecture is clearly not so much the issue of whether a canonical
standard of length can be said to have the length which it serves to define,156 as the issue
155
This much should be conceded to Gert's unorthodox reading of PI §50. See Gert (2002), (2010).
Wittgenstein even talks of “a game in which the sample is orange” (AWL p.120)
156
36
of whether saying so can count as a ground for the existential generalization to the effect
that there is something with that length. What Wittgenstein is there concerned to establish
is that the standard meter cannot be said to be one meter long in the same sense as the
sense in which for something to be one meter long is for it to make true the existential
generalization that there is something that is one meter long.
As we have seen, not only does the Tractatus not subscribe to argument A1', but it is
concerned to denounce it. Far from adhering to C1' on the basis of A1', it rejects A1' as
fallacious.157 By Tractarian lights, A1' confuses the requirement of the existence of a unit
of sense with that of an instance by excellence and therefore with that of an atom of sense.
Whether the Tractatus may be held to adhere to C1'' on the basis of A1'' is a more delicate
matter. What is clear, is that it does not subscribe to a version of argument A1'' that turns
on conflating surface-level modality and deep-level modality.158 But the Tractatus does
seem to construe units of sense as unadulterated exemplars, as if under the fantasy that a
metrical unit, while not independent from other units (i.e. an atom), could subsist apart
from any material metrical standard, because it is itself the self-subsisting canonical
standard, albeit one of a special sort, as it were an intangible metrical standard. There is
nothing wrong with holding a metrical unit to be as such intangible. It is as such
intangible. It is tangible only via the tangible standard to which, as Kripke rightly insists,
it is not identical, just as the office of a magistrate, or the honors due to its rank, are
tangible only via such things as his robe, to which they are not identical.159 But this does
not mean that we can make sense of the notion of an intangible standard or of a standard
that serves its role despite its tangibility.
Be that as it may, it can hardly be reckoned incidental that C1 is cast in the form of an
existential generalization followed by mention of its basis. Whatever the “analogous case”
may be exactly, C1 is not directly about it, for the quite simple reason that, lacking a
grammatical subject, it is not “about” anything. Although little attended to, the fact that
the logical form of C1 is, like that of C0, that of an existential generalization followed by
mention of its basis, and not that of a subject-predicate statement, is all-important, as it
directly casts doubt on the assumption that the issue over which Kripke and (most of) his
Wittgenstein opponents disagree – whether the standard meter is necessarily one meter
long or not – is of primary concern to Wittgenstein in §50. By way of consequence, it
equally undercuts the assumption that the argument to which Kripke and (some of) his
Wittgensteinian opponents alike trace Wittgenstein's alleged defense of C1 does underwrite
C1. Thus, while Kripke mislocates the rationale for C1, in denying that the argument in
question lends support to C1, he is not denying anything that Wittgenstein is asserting. The
necessity at stake in the analogous case is not the necessity for something of being so and
so, but the necessity of there being something that is so and so. Otherwise, the analogy
would indeed be a lame one, since it would involve existence on one side only, and since
the necessity operator would have different scopes on each side. This allows §50b to
engage both with the Russellian view of simplicity already faulted by Wittgenstein in the
Tractatus (and in the 1935 lectures), and with the view of simplicity at play in the
Tractatus. For, as we have seen, the simplicity of Tractarian elements does not turn on
their necessarily existing (i.e. on their existing in every possible world).
§17. According to PI §58, saying that all that “Red exists” comes to is to its being the
157
See above sections 2.2 and 2.3.
See above sections 2.3 and 2.5.
159
Thus, the objection often made to Wittgenstein's comparison of Platonic Forms with standards, to the
effect that the latter are tangible while the former are not (see e.g. Bluck (1957)), although it contains a grain
of truth, is short-sighted.
158
37
case that “ ‘Red’ has reference”, so that “Red exists” is really an attempt at talking about
linguistic use (namely about the use of the word “red”), is no safeguard against the
inclination to think that the failure of “Red exists” to make sense bespeaks the essence of
red (namely, that red exists in its own right). It may be a form of this inclination. After all,
by the early Wittgenstein's own lights, the idea that “red” is a Name – i.e. that “red”
designates a simple object – is nothing over and above the idea that “ ‘red’ has meaning”.
The claim that all that “Red exists” comes to is to its being the case that “ ‘Red’ has
reference” may be meant as the claim that this is all that “Red exists” could possibly mean
– if, per impossibile, it could mean anything; that is to say, as the claim that this is what
“Red exists” would have to mean – if, per impossibile, it could mean anything – so that
this must be what “Red exists” is trying (and failing) to say. Thus, the idea behind the
admission that “Red exists” amounts to “ ‘Red’ has reference” is that through its very
failure to make sense the sentence “Red exists” somehow manages to get across the fact
that “ ‘Red’ has reference”, together with the reason why it is impossible for it to convey
that fact directly, which is that red exists in its own right (see PI §58c).
A first step toward the realization that the fact that “Red exists” does not make sense
(assuming that it is one) does not bespeak the essence of red, lies in the realization that all
this fact comes to, is to red being a means of representation rather than something
represented, an object of comparison rather than an object. Red is but an instrument for the
making of existence-ascriptions. We are brought to this realization by being led to
recognize that the fact (assuming that it is one) that it makes no sense to say of red that it
exists could be imputed to the role which it plays in existence-ascriptions, just as the fact
that it makes no sense to say of the standard sepia (Ur-sepia) either that it is of the color
sepia or that it is not, is to be imputed to the role which it plays in color-ascriptions. This
does not show that the statement that neither being nor not-being can be attributed to an
element cannot be construed as a “metaphysical statement” about that element (i.e. as a
statement about its nature (see PI §58b)) – how on earth could one show such a thing
anyway? It is not as if we could picture to ourselves what it is that cannot be done – but it
does show that this statement need not be so construed.
Echoing back §49, Wittgenstein notes that for a verbal unit of language-game (48) to
function as a name rather than as a description of an element when uttered in a situation of
apprenticeship and instruction in the language-game, just is for that element to acquire the
status of a means of representation instead of being something represented, for that
element to behave like a name rather than like something named. From the perspective of
the learner, the elements pointed to assume the same status as the standard sepia.
Conversely, for that same verbal unit of language-game (48) to function as a description
rather than as a name of an element when uttered while engaging in the practice of the
language-game, just is for that element to have the status of something represented rather
than that of a means of representation.
A converse implication of the parallel between the elements of language-game (48) and
the standard sepia is this: just as it would be queer to regard the fact that a verbal unit of
language-game (48) functions as a name rather than as a description of an element at the
stage of apprenticeship and instruction in the language-game as a ground for saying that
“an element can only be named”, so it would be queer to take the fact that “sepia”, when it
is defined as the color of the standard sepia, functions as a name of that color, as a ground
for saying that the standard sepia can in no context be described as having the color sepia;
or, for that matter, to regard the fact that “meter”, when it is defined as the length of the
standard meter, functions as a name of that length, as a ground for saying that the standard
meter can in no context be described as being one meter long. Thus, in denying that the
statement “the standard meter is one meter long” cannot make sense Kripke is not
38
contradicting Wittgenstein. It is not that claim C1 should be read as implicitly restricted to
those contexts in which “S” can be said to name the standard meter S. For the form of C1
is emphatically unqualified and it is not by way of any such restriction that C2 qualifies C1.
What needs to be acknowledged, rather, is that Wittgenstein does not endorse C1.
That such objects as the standard sepia or the standard meter and, by way of implication,
the elements of language-game (48), are literally instruments of language, means of
representation rather than things represented, can be argued on the basis of the claim that
their names are rigid designators in Kripke's sense, that it to say, designate the same thing
in every possible world in which they designate something. In effect, the rigidity of a
designator – or at least that of a de jure designator, i.e. a designator whose “reference is
stipulated to be a single object, whether we are speaking of the actual world or of a
counterfactual situation”160 – is best conceived of in terms of the contrast between a means
of representation and something represented: a rigid designator owes its rigidity to the fact
that, for the purpose of assessing the truth-value, with respect to a possible situation, of a
statement in which it occurs, its designatum does not function as something represented
but as a means of representation. That is to say, its designatum falls on the side, not of the
situation to be measured, but on the side of the statement set against that situation to
measure it. Pursuing Wittgenstein's comparison between evaluating the truth-value of a
statement with respect to a possible situation and measuring the length of an object against
a standard of length, one might say that a rigid designator is one whose designatum
functions as a standard to be set against the world. There is thus a sense in which the
rigidity that pertains to names of units of measures is exemplary in Kripke's framework.
This feature of (de jure) rigidity is brought to the fore by Kripke when he lays stress on
the fact that even in “describing a counterfactual situation in which people, including
ourselves, did speak in a certain way different from the way we speak”, “we use English
with our meanings and our references.”161 That is why it can and must be said of a rigid de
jure designator that it “rigidly designates its referent even when we speak of
counterfactual situations where that referent would not have existed.”162 This
characterization reflects the manner in which counterfactual situations are ordinarily
evoked. We can envision a counterfactual situation in which Nixon did not win the
election without having to rely upon some qualitative specification of what it is to count as
being Nixon in a possible world, because we can simply “stipulate that, in talking about
what would have happened to Nixon in a certain counterfactual situation, we are talking
about what would have happened to him.”163 The counterfactual possibility that Nixon did
not win the elections “need not be identified with the possibility of a man looking like
such and such, or holding such and such political views, or otherwise qualitatively
described, having lost. We can [for example] point to the man, and ask what might have
happened to him, had events been different.”164 Thus, the problem of the identification of
individuals across possible worlds simply need not arise.
As Kaplan has argued, the above feature of rigidity is best brought out by marking the
distinction, only implicit in Kripke, between the context in which a sentence is uttered and
the circumstances with respect to which its truth-value is assessed, and by supplementing
Kripke's “picture of possible worlds” with the “picture of structured propositions”,
according to which the designata of (what Kaplan calls) “directly referential terms”
literally figure in the propositions expressed by sentences in which those terms occur.
160
Kripke NN p.21 note 21.
Kripke NN p.77.
162
Kripke NN p.21 note 21.
163
Kripke NN p.44.
164
Kripke NN p.46.
161
39
(Kaplan has a vivid way of putting the point: “That's right, Nixon himself, trapped in a
proposition.”165) Like a singular de jure rigid designator in Kripke's sense, a directly
referential term “designate[s] the same individual in all possible worlds whether the
individual 'exists' or not.”166 But it does so in virtue of the fact that “its referent, once
determined, is taken as fixed for all possible circumstances, i.e., is taken as being the
propositional component.”167 What the picture of structured propositions makes
perspicuous, is how a directly referential term can refer without first passing through the
proposition, that is to say, without the mediation of a component of the content of what is
being said.168
For me, the intuitive idea is not that of an expression which turns out to designate the
same object in all possible circumstances, but an expression whose semantical rules
provide directly that the referent in all possible circumstances is fixed to be the actual
referent.169
If the individual is loaded into the proposition (to serve as the propositional
component) before the proposition begins its round-the-worlds journey, it is hardly
surprising that the proposition manages to find that same individual at all of its stops,
even those in which the individual had no prior, native presence. The proposition
conducted no search for a native who meets propositional specifications: it simply
“discovered” what it had carried in. In this way we achieve rigid designation. Indeed,
we achieve the characteristic, direct reference, form of rigid designation, in which it is
irrelevant whether the individual exists in the world at which the proposition is
evaluated.170
In the light of this picture of rigidity, the free variable under an assignment, or dummy
name, “which designates the same individual in all possible worlds, whether the
individual ‘exists’ or not”171, proves to be the paradigm of rigid designation:
In evaluating “Fx” at a world w, we do not ask whether its value exists in w, we only
ask what value was assigned to the variable before the process of evaluation at w
began. Until a value is assigned we have nothing to evaluate. Furthermore, and this is
important, it is irrelevant how “x” gets its value, how the assignment is made, how
the value of “x” is described when it is assigned to “x”. All that matters to the
evaluation is that “x” has a particular value.172
The counterfactual claim adduced in support of the claim that “existence cannot be
attributed to an element”, namely the claim that “If it did not exist, one could not even
name it and so one could say nothing at all of it”, turns out either to evince a confusion or
to reduce to a truism. It evinces confusion if it turns on the idea that, in the counterfactual
circumstance that an element did not exist, there would be nothing for its name to
designate. And it reduces to a truism if it is merely meant to register the fact that only
what actually exists is actually available for being used as a means of representation. The
truism is best expressed by saying that if this thing did not exist, we would not use it. As to
the confusion, it comes from identifying “what people would have said in certain
circumstances, had those circumstances obtained, with what we would say of certain
165
Kaplan (1978) p.13.
Kaplan (1989a) p.493.
167
Kaplan (1989a) p.493.
168
See Kaplan (1989b) p.568-569.
169
Kaplan (1989a) p.493.
170
Kaplan (1989b) p.569.
171
Kaplan (1989a) p.493.
172
Kaplan (1989b) p.571-572.
166
40
circumstances, knowing or believing that these circumstances don’t obtain.”173 From the
premise that “to use ‘Moses’ as a name, there has got to be an object referred to, namely
Moses”, we are tempted to infer that the sentence “Moses does not exist” could not have
been true by the following pattern of reasoning: “if there hadn’t been a Moses, we
wouldn’t have been able to use this name; we wouldn’t have been able to say so; and
perhaps even the proposition that Moses doesn’t exist itself wouldn’t have existed.”174 But
the point is that we do have the name ‘Moses’ at hand, and that it is part of our language
whether it would have been part of our language in counterfactual circumstances or not. In
fact, “If you say: ‘Suppose Hitler had never been born’, then ‘Hitler’ refers here, still
rigidly, to something that would not exist in the counterfactual situation described.”175 In
other words, “under certain circumstances what is expressed by ‘Hitler does not exist’
would have been true, not because ‘Hitler’ would have designated nothing (in that case we
might have given the sentence no truth-value) but because what ‘Hitler’ would have
designated – namely Hitler – would not have existed.”176 Together with this pattern of
reasoning, one reason for denying that existence is a first-level predicate falls to the
ground.177 And to dispose of the latter is to dispose of one reason for holding the analogy
of PI §50 to be impaired by the fact that it treats existence on a par with first-level
predicates.
Through the distinction between the context in which a proposition is uttered and the
circumstances at which it is evaluated, the apparatus of direct reference makes wholly
perspicuous the difference of level between naming and describing – which is brought out
in PI §49 in connection with language-game (48) – by displaying the sense in which
“naming is a preparation for describing”, “so far not a move in the language-game”
(PI §49):178
When the individual is determined (when “the reference is fixed”, in the language of
Saul Kripke), it is loaded in the proposition. It is this that makes the referent prior to
the propositional component, and it is this that reverses the arrow from propositional
component to individual in the Direct Reference picture.179
A benefit of thinking of the means of representation into which an element is turned as it
is introduced through its name, on the model of a metrical standard, is that it may help us
to bring out the sense in which an element can be compared to itself. For there is a sense
in which a standard can be compared to itself, that is to say, a sense in which one can talk
of a standard being set against itself. Or at any rate there is one if Kripke is right in his
claim that the definition of the name of a unit of measure does not supply a synonym for it
but only fixes its reference. Stick S was not turned into the standard meter by being
assessed with respect to its length; nor was it assessed with respect to its length in being
turned into the standard meter. But not only does this not preclude S, as the standard
meter, from being assessed with respect to its length as long as it is not used as means of
representation, but this does preclude S from being usable, as the standard meter, to assess
itself, as something that is not a means of representation, with respect to its length. It
173
Kripke RE chap.2.
Kripke RE chap.2.
175
Kripke NN p.78.
176
Kaplan (1989a) p.492-493.
177
See Kripke RE chap.2.
178
There is however something that stands in the way of a full endorsement by Kripke of Kaplan's
reconception of rigidity as direct reference, at least as it stands: namely, that the apparatus of direct reference
masks the fact that there is no such thing as counterfactual existence, for the simple reason that the actual
world is the only one there is. For Kripke, as for the early Wittgenstein, only of the world – i.e. of the actual
world – can it be said that it “is all that is the case”.
179
Kaplan (1989b) p.569.
174
41
makes sense to say, if only because it is true, that S could have failed to be one meter long,
i.e. that one meter could have failed to be the length of S. What makes this counterfactual
circumstance describable is that S in its actual condition (including its actual length), once
it has been “loaded into” language (once its length has been fixed as the reference of
“meter) and to that extent “withdrawn from” the realm of the represented (i.e. the realm of
circumstances), can be used to represent itself, S, as not being a certain way in a certain
circumstance. Likewise, an element is not turned into a means of representation by being
represented; nor is it represented in being turned into a means of representation. But not
only does this not preclude an element from being represented (described) as long as it is
not used as a means of representation (named), but this does not preclude it from being
usable, as a means of representation, to represent itself, as something that is not a means
of representation, as not being a certain way (or even as not being at all) in a certain
circumstance. Thus, to grant that something cannot be used at the same time as a means of
representation and as something represented is not enough. At most, it could be said that
something cannot be used at the same time and in the same respect as a means of
representation and as something represented. But this, of course, is no more than a way of
rephrasing the distinction between a means of representation and something represented.
§18. The last tract of §50c preempts a natural misunderstanding of the deflationary point
so far pressed in that paragraph, one that the formulations so far adduced court. As is
emphatically clear from this last stretch, the ultimate point of §50 is not that what, on the
face of it, there has to be, is really an object of comparison rather than an object, a means
of representation rather than something represented. The truly deflationary lesson of §50 is
that to say that what, apparently, there has to be, is really a means of representation, is
merely to say that it is really a means of representation of ours, something we have turned
into such a means, an object of comparison set by us. It counts as a means of
representation only insofar as we count it as so. It is our method of representation that
dictates – that is to say, us who dictate – which means of representation we employ, not
the other way around. Registering that what, apparently, there has to be, is really part of
the language, is compatible with regarding it as indispensable to language, as necessary to
the fulfillment of one of its internal ends. The concession may be only apparent and really
subserve such a picture. The claim that all that “Red exists” comes to is to its being the
case that “ 'Red' has reference” is then supposed to reflect the fact that red exists in its own
right in language – that it is an indispensable element of any language in which one can
talk about red. It is as if red, being what it is, were necessarily part of our language, at
least insofar as it is a language in which it is possible to talk about red. The illusion is a
teleological one. It is as if red were designed to endow “red” with a meaning by becoming
part of our language, and as if, conversely, “red” thereby got the very meaning that it was
designed to acquire. That we could not think anything to be red if red did not exist does
not establish that red must be a sample in our language if “red” is to have a meaning
within it; for if red did not exist, then another language would be our language.180
Here we touch upon a second benefit of conceiving on the model of a metrical standard
the means of representation into which an element is turned as it is introduced through its
name. The definition of a unit of measure is notoriously stipulative. It is, in that sense,
notoriously arbitrary. “Meter” could have been stipulated to refer to another length.
Convenience aside, a rigid stick of any length would have done the job. Whether or not it
180
Wittgenstein PG §95 p.143: “ 'I could not think that something is red if red did not exist.' What that
sentence really means is the representation of something red, or the existence of a red sample as part of our
language. But of course one cannot say that our language has to contain such a sample; if it did not contain
it, it would be, precisely, another language. But one can say and emphasize that it does contain it.”
42
is an accident that “meter” refers to this length, which it was stipulated to refer to (it is not
an accident if “meter” is a rigid designator), it is certainly an accident that “meter” was
stipulated to refer to it. (Note that the point is not simply the trivial one (which has nothing
particularly to do with stipulation) that “meter” could have been stipulated to refer to
another thing, in the sense in which we could have called “red” what we actually call
“green”. In the relevant sense, “meter” could not have been stipulated to refer to just any
other thing, but it could have been stipulated to refer to another length.) The definition of
that unit of length is, to that extent, not answerable to anything. And so we not too
tempted to regard the object through which it was defined (or even, for that matter, the
class of the objects with the same length) as uniquely amenable to this definition and
therefore indispensable to our language. The choice never was one between resorting to
this stick (or, for that matter, to a stick of this length, i.e. of the same length as this stick)
and not resorting to it, but between resorting to this stick (or to a stick of this length) and
resorting to one of another length. Only through some kind of retrospective illusion might
it come to look otherwise.181
Yet the benefit of adverting to the coordinative definition of the name of unit of measure
will be lost if, flouting Kripke’s cautions, we take it to supply a synonym for it. For
suppose that “meter” is synonymous with “the length of S at t0”. Then that there is a stick
with the length called “meter”, namely the standard meter S (at t0), is part of the meaning
of “meter”. But then it is not an accidental property of the length called “meter” that there
be a stick with that length, namely the standard meter S (at t0). So if S did not exist, so that
there were no stick with that length, then that length itself would not exist: there would be
no such thing as the unit of length called “meter”. And it now begins to look as if the
standard meter had to be part of our language if “meter” is to mean anything at all.
Conversely, since the length of a stick is not an essential property of it, if “meter” is not
stipulated to mean “the length of S at t0” but only stipulated to refer to the length of S at t0,
181
Presumably, the point of resorting to a color-word like “sepia”, rather than to a color-word like, say,
“red” (or even “fuchsia”), for the purpose of canvassing a language-game in which a color-word is
stipulatively defined as the color of a certain object erected into a standard, is that ascriptions of the
particular shade of brown ordinarily called “sepia” seem inherently subject to uncertainty and disagreement,
in a way ascriptions of most colors and color-shades do not. This makes it intelligible why we might
arbitrarily select some brownish object for being the standard for that color: such a convention would allow
us to dispel some uncertainties and to settle some disputes. Were we asked instead to envision a languagegame in which “red” is defined as the color of a certain object erected into a standard, we would be hard put
to forego the feeling that something about its nature – namely its color – somehow made the object selected
as standard fit for being selected as the standard. Precisely because ascriptions of “red” do not seem
inherently subject to uncertainty and disagreement in the way ascriptions of “sepia” seem to be, even though
the reference of “red” is not, in fact, stipulated via a description, it would keep looking as if the standard for
red had been selected on account of the color which it exemplified and hence possessed – as if it were, as it
were, already somehow a sample of red before it was erected into the sample for red. (After all, this is
indeed how samples are selected in the course of ostensive teaching. Ostensive teaching relies on some
objects already counting as samples from the perspective of the teacher. It does not erect such objects into
samples except from the perspective of the pupil.) On the other hand, the illusion that the standard for a
certain color is indispensable to (our) language, if ascriptions of that color are to be possible, is perhaps
nowhere stronger than in the case of a color-word which, like “sepia” (or “fuchsia”, for that matter)
designates a very particular color-shade, one that seems so determinate to us that it cannot be explained
except by means of an equally determinate sample. This particular shade, we are inclined to think, could not
have been defined except by pointing to this standard. So, alternatively, the point of resorting to a colorword like “sepia” might be that it invites, even more than a color-word like “red”, the very teleological
illusion which a word like “meter”, whose ostensive definition is notoriously arbitrary, may help us to
dismantle. Either way, it is crucial that we should conceive of the fixation of the reference of “sepia” strictly
on the model of that of “meter”. As long as we shall do so, we shall not be tempted to regard the object to
which the name “sepia” is coordinated (i.e. the standard sepia) as giving a meaning to that name. By parity,
we shall not be tempted to regard an element of language-game (48) as providing its name with a meaning.
43
then it is only an accidental property of the length called “meter” that there happens to be
a stick with that length, namely the standard meter S (at t0). The unit of length that we call
“meter” could have been defined via another accidental property (say, that there is another
stick, S', with that length). So, even if there is only one standard, in the counterfactual
circumstance that S did not exist, “meter” could still have been defined as that length,
which it was defined as. Given the way “meter” is defined (i.e. its reference is fixed), it is
not conceivable that S should turn out not to be one meter long at t0: that is to say, it makes
no sense to talk of S turning out not to be one meter long at t0 after all. But this does not
mean that “S is one meter long” is necessary, i.e. that S could not have failed to be one
meter long.
Note that saying that it is not essential to the length as which “meter” is defined that it
should be the length of stick S does not mean that, strictly speaking, only the actual length
of S – not S itself – becomes an instrument of language upon S being erected into the
standard meter: what it does mean, is that only the standard meter as it actually is, i.e. S in
its actual condition, becomes such an instrument.
Although stick S serves to stipulate the length to which “meter” is to refer and S
exemplifies that length, S is but a dispensable means of fixing the reference of “meter”,
just like any part of any device for fixing the reference of a term. In that sense, not only
does S contribute to no provision of meaning, but also it is unessential to even that to
which it does contribute, namely the fixation of the reference. But this by no means
betrays some inclination, on Kripke's part, to regard examples as mere expedients that can
facilitate, but not replace, the direct grasp of what they are meant to exemplify, indirect
ways of attaining something which lies beyond them and which, on their own, they
necessarily fall short of conveying.182 S is indeed a mere crutch. But, first, S is not in fact
an instance of the property designated by “meter”, for the simple reason that “meter” does
not designate a property, but an (abstract) object. Second, the procedure for fixing the
reference to which S is instrumental is precisely unrepresentative, because exceptional:
generally, the reference of a name is not fixed via a description or even via a cluster of
descriptions.
Kripke only considers names whose reference is stipulated by description in order to
show that even if the reference of a name was typically stipulated by means of a
description or a cluster of descriptions, that description or cluster of descriptions would
still be unessential to the meaning of the name. No description is ever an indispensable
way of fixing the reference of a name because no description is ever an indispensable part
of its meaning – even when that description is actually used to stipulate what the name is
to refer to and in that sense holds a priori of its referent.
Far from decrying the instances of a property as being mere crutches, Kripke famously
traces the rigidity of various common names to the fact that their actual paradigmatic
instances constitute the depository and the standard of their use. It is because the standard
for being-a-cat is none other than our cats, that is to say the things we actually call “cats”,
that, given that we have not found our cats not to be animals, we cannot so much as make
sense of the possibility that something had been an automaton, yet a cat. (To acknowledge
that cats could have turned out not to be animals but sophisticated automata is not to admit
that there could have been things that were automata, yet were cats, but to admit that there
could have been things that looked like cats (i.e. were “evidential counterparts” of cats) –
that is to say, that looked like our cats – yet were automata.) And it is for the same reason
that, were we to find out that our cats are not in fact animals but sophisticated automata,
we would not conclude that there are no cats after all, but rather that cats have proved not
182
For this charge, see Diamond (2001).
44
to be animals and that, to the extent that we can be said to have taken for granted that they
were, we can be said to have been mistaken about them.
It is at best misleading to hold the deflationary point of PI §50 to be that C1 amounts to
the claim that the standard meter S is a condition of possibility of the game of measuring
in virtue of its being “what gives 'meter' a sense”, so that to imagine that S did not exist is
to imagine that the world “be such that it would be impossible to formulate metrical
propositions.”183 Wittgenstein is not trying to reconcile us with the alleged truism that “if
it were not for the standard meter, 'meter' would have no meaning”,184 but rather to alert us
to the metaphysical urge which lurks in such a counterfactual claim. For this
counterfactual makes it seem as if the standard meter S, upon being brought in, “gave
content to “meter” where before it was empty.”185 Whereas S can only be said “to give
'meter' a sense” “in the sense of enlarging the game”: in introducing S as the standard, “we
have altered the game.”186
The iteration of modalities that typically attends such counterfactuals as the one just
mentioned – as in the idea that “the determination of sense and also the distinction
between necessity and contingency rest on a foundation of contingent fact” – is of the sort
traced by Kripke to a misconception of the conjunction of an epistemic modality and the
negation of the corresponding non-epistemic modality.
This is not to deny that PI has room for the idea that our standards of sense could prove
hostage to worldly contingencies. But this idea is not a concern of PI §50. And it should
precisely not be conflated with the idea that our standards of sense always already
presuppose the not obtaining of certain worldly contingencies.187
It bears emphasizing that if “meter” meant “the length of S at t0” in the sense of being
synonymous with “the length of S at t0”, then “meter” would have other referents than its
actual referent in counterfactual worlds where the length of S at t0 differs from its actual
length, and no referent at all in counterfactual worlds where S fails to exist. “Meter” would
hardly behave like a name, let alone like the name for an element, since what it would
designate would fail to be inalterable, let alone indestructible. One blind spot of the
Tractatus was its twofold assumption that an object is not nameable unless it is simple and
that an object is not simple if it is analyzable (i.e. definable) via a description.188 To
ascribe to PI §50 the view that “meter” is defined as synonymous with “the length of S at
t0” is to take PI to hold this pair of assumptions in place. It is, by the same token, to ignore
the fact that a commitment to this pair of assumptions seriously impairs the analogy on
which PI §50 turns. Conversely, if this analogy is not in fact defective in such manner,
then it undermines this pair of assumptions.
A third benefit of conceiving the means of representation into which an element is
turned, as it is introduced through its name, as a metrical standard, is that it may guard us
against the temptation to conflate the correct idea that there is no single way for sense and
existence to articulate into units with the incorrect idea that sense and existence
themselves are matters of convention. Again, this benefit is spoiled in ovo if, ignoring
Kripke's animadversions, we take the coordinative definition of the name of a unit of
measure to supply a synonym for it. For suppose that “meter” meant “the length of S at t0”
in the sense of being synonymous with “the length of S at t0”. Then there is no such thing
as the length in meters of an object simpliciter. The length in meters of an object is
183
Jolley (2010) p.127. My emphasis.
Gert (2002) p.65. Jolley subscribes to Gert's remark on p.121 of Jolley (2010).
185
Wittgenstein AWL p.142.
186
Wittgenstein AWL p.143.
187
As suggested in White (1972).
188
See Ishiguro (1969).
184
45
relative to the length of S. A fortiori, there is no such thing as the length of an object
simpliciter. The length of an object is relative to a unit of measure, which is relative to a
standard.
The two illusions which the comparison of elements with standards of measure is meant
to forestall fuel each other. They are but the two poles of a single oscillation. Like
Wittgenstein, Kripke is concerned with dislodging the temptation to think of the rigidity
(i.e. determinacy) of sense as some sort of super-rigidity, as the sublimation of the
empirical rigidity possessed by a measuring stick. The rigidity of sense is not a matter of
indestructibility or timelessness (compare PI §58b).
§19. Its dialectical method notwithstanding, the Tractatus is unreservedly committed to
the conception of simplicity invited by Socrates’ dream at least to this extent, that it
sanctions a dichotomy between saying and naming – between the inherent articulateness
of the former and the equally inherent inarticulateness of the latter. This dichotomy finds
expression in the denial that it makes sense to negate a name. No doubt we are meant to
realize that such a denial in turn fails to make sense, just as we are meant to realize that
the categorial distinction between objects and facts – the single categorial distinction in
favor of which all categorial distinctions are relinquished in the Tractatus – is one that
gets expressed in language, rather than one that we can ourselves undertake to express.
But this leaves the dichotomy intact. The dichotomy is reflected by the grammar of
language. Our capacity to make any sense at all is unintelligible apart from the possibility
of names – symbols that it makes no sense to negate.
Such a picture of what it takes for sense to be determinate that is the target of PI §50. It is
not the dichotomy by itself so much as its point and status that PI §50 questions. PI §50
does not argue for a conventionalist account of existence. It follows through the
consequences of the Tractatus’ insight into the difference between names and sentences
up to the point where that insight undoes itself. What the Tractatus half-realized, but halfrealized only, is that the difference between names and sentences, like all grammatical
differences, is a difference of level. In the Tractatus, already, for facts not to be simple is
not for them to be complex, hence not for them to be complexes, hence not for them not to
be simples. If facts and objects, however, do not display contrary features (be they
formal), then not only are pseudo-observations like “names cannot be negated”, or
“elements cannot be said to be or not to be”, or “facts cannot be named”, and so on,
ultimately unintelligible, but they are as gratuitous as “Roses have no teeth”. Not only can
the point of uttering such remarks only be transitional, but also it can only be relative to
some definite elucidatory purpose.
There is, in the absolute, absolutely nothing that cannot be done with names or, for that
matter, with elements. Saying that “elements can only be named” – that “they cannot be
described”, that “they cannot be said to be or not to be” – makes it look as if the range of
what can be done with elements were restricted, as if nameables were deprived of the
features characterizing sayables and vice versa. But elements are no more deprived of the
aforementioned possibilities than roses are deprived from having teeth. Likewise, the
denial that names could be negated is, in the absolute, wholly gratuitous, like the denial
that an elephant could pass through the eye of a needle. It registers no privation on the part
of names and their bearers.
Since “naming and describing do not stand at the same level” (PI §49) – naming being, in
a way, but a preparation, at the stage of the instruction into the language-game, for the
descriptive moves subsequently taken within the practice of that language-game189 – that
189
That this point is of crucial importance is well brought out by Jolley. See Jolley (2010) pp.110-111,
p.117.
46
names do not count as descriptions at the stage of instruction offers no ground for holding
that “elements can only be named”, and is wholly compatible with names counting as
descriptions (if only as degenerate ones) at the stage of practice190. Is this to say that
elements can be described after all, and that the Tractatus went astray insofar at it
intimated the opposite? Did the Tractatus simply overlook the possibility of devising a
language-game disproving the alleged impossibility?191 Or shall we hold the fact that
“naming and describing do not stand at the same level” to offer on the contrary renewed
ground for the claim that “elements can only be named”, insofar as it supports a revised
(because restricted) version of it, according to which “at the stage of instruction elements
can only be named”?192 Shall we insist that it is not the same symbol, but only the same
sign, that may count, now as a name of an element (at the stage of instruction), now as a
description of it (at the stage of practice)? But the difference of level between naming and
saying is flattened out in the same proportion by the claim that “elements can be described
after all”, as by the claim that it means to dislodge, to the effect that “elements can only be
named”. And the insistence that in making use of one and the same sign, now to name an
element at the stage of instruction, now to describe it at the stage of practice, one
essentially makes two distinct uses of it, ignores that we can have no grasp of what it is for
two uses of the same sign to count as identical or not apart from an understanding of what
it takes to be using a sign in the same way in two contexts.
The point of §§46-50 is not that it is not impossible (let alone nonsensical) after all to
attribute being or non-being to elements (or that one can devise a language-game falsifying
the claim that it is), as the anti-standard reading would have it. But neither is it simply that
the impossibility (or nonsense) in question is not substantial, as standard readings
maintain. If it were, then PI §50 would have to be read as offering either a good defense of
the Tractatus’ view of simplicity or a bad attack (because off-target) on it. For, as we have
seen, there is little doubt that the view of simplicity standardly ascribed to PI §50 is, in its
essentials, already to be found in the Tractatus.
References
Ahmed, Arif (2010)
Wittgenstein's Philosophical Investigations: a Reader's Guide.
Continuum.
Anscombe, Elisabeth (2011) From Plato to Wittgenstein. Exeter: Imprint Academic.
Avital, Doron (2008)
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